D420 Discrete Math: Logic, catalog number MATH 2820, is a one-CU module covering logic, proofs and Boolean algebra. It is the first of three one-CU modules that together replace the older four-CU C959, and its small size is deceptive. One competency unit of logic is still the foundation the other two modules and everything in the second discrete course stand on.
What one competency unit actually means here
A one-CU course is a real course with a real assessment, not a formality. What the smaller size changes is the shape of your plan. There is no long ramp, no comfortable middle weeks, and very little room to be behind. The whole module can be closed inside a fortnight of focused work by a student who starts correctly, and it can stretch to two months for a student who tries to absorb logic by reading.
The other consequence is that everything in the module is load-bearing. In a four-CU course you can be shaky on one topic and still pass. Here the topic list is short enough that each item is likely to appear, so the plan is to make all of it solid rather than to triage.
D420 and the C959 arrangement
WGU carries both arrangements of this material in the catalog. C959 Discrete Mathematics I under MATH 2800 is the four-CU course covering logic, proofs, Boolean algebra, set theory, sequences, series, relations, graphs and trees in one run. D420 is the first slice of that, with D421 Discrete Math: Functions and Relations and D422 Discrete Math: Algorithms and Cryptography taking the rest.
That means resources written for the logic chapters of the older course apply directly here, which widens your options considerably. Check your own Course of Study for the competency list and the assessment, since those belong to the code on your Degree Plan rather than to the material.
Logic is translation before it is anything else
The mechanical part of propositional logic gives almost nobody trouble. Truth tables are bookkeeping. What separates students is translation: turning an English sentence into symbols without losing or adding meaning.
Three traps account for most translation errors. First, unless is not the same as if. The sentence saying you cannot enter unless you have a pass is a conditional, and getting its direction backwards inverts the whole statement. Second, only if points the arrow the other way from if, which is the single most common symbolic error in this material. Third, English uses or inclusively and exclusively without marking which, so the sentence has to be read for intent before it is symbolised.
Predicate logic adds quantifiers and a fourth trap: order matters. The statement saying that for every person there exists a key that opens their door is not the same as the statement saying that there exists a key that opens every person's door. Swapping the quantifiers changes a claim about many keys into a claim about one master key. Practising that swap deliberately, on ten sentences, is worth more than any amount of reading about quantifiers.
A plan sized to one competency unit
Open your Course of Study before planning. WGU keeps the competency list and assessment detail there and not in the public catalog. Where a performance assessment exists, each scored aspect is judged on its own three-point scale and a score of 2 in each passes the task. Where the instrument is a proctored objective assessment, the preassessment is your diagnostic.
A worked plan with numbers. Four blocks fit one competency unit: propositional logic and truth tables, logical equivalences, predicate logic and quantifiers, and proof methods with Boolean algebra. At sixteen to twenty hours total, that is four to five hours per block. Inside each, spend one hour on the concept, two and a half on problems, and half an hour writing your own summary in words. That last half hour per block gives you a two-page reference sheet in your own language by the end, which is what you revise from.
Where a written task exists, the word budget is correspondingly tight. Four scored aspects across a 900-word submission is about 200 words each after an opening and a close. In logic that is generous, because a correct symbolisation plus a justification is short. Length is not the risk here. Precision is.
How to lay out logic work
Where directions set a format, follow it. Otherwise this order makes logic work checkable line by line.
| Step | What appears | Why it is scored |
|---|---|---|
| Atomic statements | Each simple proposition given a letter and a plain-English meaning | Without the key, no reader can verify a symbolisation |
| Symbolisation | The full statement in symbols | The translation itself is usually the assessed skill |
| Justification | One sentence on why the connective or quantifier order was chosen | Separates a correct guess from a correct reading |
| Truth table or derivation | All rows, or the equivalence chain with each law named | Named laws are what make a derivation an argument |
| Result | Tautology, contradiction, contingency, or the simplified expression | Stating the classification, not just producing the table |
| Boolean form | Where circuits are involved, the simplified expression with the law used at each step | Simplification without justification cannot be followed |
| Plain-English reading | The final expression translated back into a sentence | Proves the symbols still mean what the problem meant |
The final row is a habit worth keeping permanently. Translating your answer back into English catches errors that no amount of checking symbols will, because a symbolisation can be internally consistent and still say something the original sentence never claimed.
Practice habits for a short, dense module
- Build truth tables in a fixed column order every time. Consistency turns a slow task into a mechanical one and prevents dropped rows.
- Memorise a small set of equivalences and derive the rest. De Morgan's laws and the conditional rewritten as a disjunction cover most of what you will need.
- Name every law you apply in a derivation. An unnamed step is unverifiable and usually unscored.
- Write the negation of every statement you meet. Negating quantified statements correctly is a skill that appears throughout the rest of discrete mathematics.
- Do Boolean algebra and propositional logic side by side. They are the same structure with different symbols, and seeing that halves the memorisation.
- Test symbolisations against a case. Pick truth values that make the English sentence false and check your symbols agree.
What Competent looks like in D420
Results in this module are Competent or Not Competent. WGU issues no letter grades and holds no ordinary grade point average, performance assessment work can be revised and resubmitted with no penalty for the first version, and any objective assessment is proctored and yours alone to sit.
Logic work that passes cleanly tends to show:
- A statement key defining every letter before any symbols appear.
- Conditional direction handled correctly, including for only if and unless.
- Quantifier order preserved, with nesting written out rather than assumed.
- Every equivalence step labelled with the law that justifies it.
- A stated classification or simplified result rather than a table left for the reader to interpret.
Proctored assessments are yours to sit and that does not change. We prepare with symbolisation drills, equivalence practice, worked derivations and timed sets, and we give an honest readiness read. We do not sit or assist during an assessment and we never ask for portal credentials.
Five mistakes that cost time in D420
- Reversing a conditional. Only if and if point in opposite directions, and this single error accounts for a large share of wrong symbolisations.
- Confusing the converse with the contrapositive. One is logically equivalent to the original and one is not, and the confusion propagates into every proof you write later.
- Swapping nested quantifiers. The two orders make genuinely different claims, and the difference is invisible if you never write both out.
- Treating a truth table as an answer. The table is evidence. The answer is the classification or the equivalence it establishes.
- Underestimating one competency unit. The module is small, not easy, and everything in it appears again in the modules that follow.
How support works on this course
Send your competency list, any preassessment result and any task directions from your Course of Study. What comes back is sized to a one-CU module: a symbolisation drill set built around the traps that actually cause errors, an equivalence sheet you can derive rather than memorise, worked derivations with every law named, and where a written task exists, a model submission answering each aspect under its own heading.
Terms at WGU run six months at a flat rate, so the courses you close inside a term are what lower your effective cost per course. One-CU modules are the clearest illustration of that arithmetic: three of them closed in a month is three courses off the plan, and the logic module is the one that makes the other two faster.
Questions students ask about D420
Is D420 the same as MATH 2820?
How does D420 relate to C959?
Can a one-CU course really take only a couple of weeks?
One competency unit, and the quantifiers keep flipping?
Send your competency list. You get symbolisation drills built around the real traps, a derivable equivalence sheet and worked derivations with every law named.
Where D420 sits in WGU's programs
The July 2026 catalog places this code in 2 current WGU programs. Open a program page for the complete standard path and term positions. The live Degree Plan remains authoritative after transfer credit, substitutions, and mentor planning.
The assessments, one by one
The public catalog does not publish this course's PA/OA identity or task count. WGU Tutors publishes at most one PA manual per course and only from a WGU-controlled public rubric. Until that source exists, PA help begins from the student's real Course of Study and OA support remains preparation only.