ACSEE (Form 6) Logic — practice questions

Explore 2 free Logic questions in ACSEE (Form 6) Advanced Mathematics. Open each question or exercise to read its content, reference answers and available explanation.

Practise Logic with Quill →

Logic questions and exercises with answers

Showing questions 1–2 of 2.

Using the laws of propositions of algebra, $(P\rightarrow(Q\vee\sim R))\rightarrow(P\wedge Q)$ simplifies to:Read the answer and worked solution →Match the rule of inferenceRead the answer and worked solution →

Worked practice questions

Using the laws of propositions of algebra, $(P\rightarrow(Q\vee\sim R))\rightarrow(P\wedge Q)$ simplifies to:

$P\vee(Q\wedge R)$
$\sim P\vee(Q\wedge R)$
$P\wedge(Q\wedge R)$
$P\wedge(Q\vee R)$

Show answer and solution

Correct answer: D. $P\wedge(Q\vee R)$

1. Replace the inner conditional using $A\rightarrow B\equiv\;\sim A\vee B$: the antecedent becomes $\sim P\vee(Q\vee\sim R)$. 2. Apply the same rule to the outer conditional, negating that whole antecedent. 3. De Morgan's law turns $\sim(\sim P\vee Q\vee\sim R)$ into $P\wedge\sim Q\wedge R$. 4. The statement is now $(P\wedge\sim Q\wedge R)\vee(P\wedge Q)$, and $P$ factors out. 5. The bracket $(\sim Q\wedge R)\vee Q$ absorbs to $Q\vee R$, leaving $P\wedge(Q\vee R)$. _Source: NECTA ACSEE 2023 Advanced Mathematics 142/2, Question 2: Logic_

Open this question →

Match the rule of inference

Read exercise and reference answers

Matching pairs

Left
P → Q, P ⊢ Q
Right
Modus ponens
Left
P → Q, ~Q ⊢ ~P
Right
Modus tollens
Left
P ∨ R, ~P ⊢ R
Right
Disjunctive syllogism

Instructions

Tap a pattern on the left, then the rule that names it.

Open this exercise →

How to practise

Choose a Logic question and try to work out your answer.
Open the question to check the correct answer and read its worked solution.
Continue in the app for bite-sized lessons, explanations and review with Quill. You can start without creating an account.

Put it into practice

Continue with Logic practice for ACSEE (Form 6). Read explanations as you go. No signup form needed to start.

Practise Logic →