alleryStart learning →The statement pattern p ∧ q is a
- tautology
- contradiction
- dual pair
- contingency
Show answer and solution
Correct answer: D. contingency
It is true when both are true and false otherwise, so it is a contingency.
MHT-CET Mathematical Logic — practice questions — page 2
Explore 57 free Mathematical Logic questions in MHT-CET Mathematics. Open each question or exercise to read its content, reference answers and available explanation.
Practise Mathematical Logic with Quill →Mathematical Logic questions and exercises with answers
Showing questions 31–57 of 57.
The statement pattern p ∧ q is aRead the answer and worked solution →Two statement patterns are logically equivalent if theirRead the answer and worked solution →A statement pattern has 3 prime components. How many combinations of truth values are possible?Read the answer and worked solution →The symbols ∃ and ∀ are calledRead the answer and worked solution →The phrase "there exists" is called theRead the answer and worked solution →When does a 'for all' claim about a collection turn out false?Read the answer and worked solution →Take A = {1, 2, 3, 4, 5, 6, 7}. The claim 'some x in A has x – 4 = 3' isRead the answer and worked solution →The dual of the compound statement p ∨ q isRead the answer and worked solution →Interchanging ∧ and ∨ in (p ∧ q) ∨ r producesRead the answer and worked solution →Writing the dual of t ∨ p, we getRead the answer and worked solution →In forming a dual, the letters t and c areRead the answer and worked solution →The equivalences ~(p ∧ q) ≡ ~p ∨ ~q and ~(p ∨ q) ≡ ~p ∧ ~q are known asRead the answer and worked solution →To deny 'if p then q', we assertRead the answer and worked solution →Negate: 7 > 3 and 4 > 11. The result readsRead the answer and worked solution →The negation of "The number is neither odd nor a perfect square" isRead the answer and worked solution →Swapping the two parts of p → q givesRead the answer and worked solution →Negating both parts of p → q, in place, givesRead the answer and worked solution →If p is true and q is false, the converse q → p has truth valueRead the answer and worked solution →Which statement is logically equivalent to p → q?Read the answer and worked solution →Rewriting an implication p → q using only ~ and ∨ givesRead the answer and worked solution →Rewriting 'p if and only if q' using implications givesRead the answer and worked solution →Simplify p ∨ (p ∧ q) using absorption:Read the answer and worked solution →Joining any statement p with a tautology by 'or' always yieldsRead the answer and worked solution →Two switches wired one after another, in series, act likeRead the answer and worked solution →Two switches wired side by side, in parallel, act likeRead the answer and worked solution →In switching tests, the value 1 stands for a switch that isRead the answer and worked solution →The lamp in a parallel circuit of two switches is off only whenRead the answer and worked solution →
Worked practice questions
Two statement patterns are logically equivalent if their
- truth values match always
- symbols look identical
- letters are equal in number
- first rows agree fully
Show answer and solution
Correct answer: A. truth values match always
Equivalence means identical truth values for every combination of components.
A statement pattern has 3 prime components. How many combinations of truth values are possible?
- 6
- 9
- 12
- 8
Show answer and solution
Correct answer: D. 8
Each component is T or F, so 2 × 2 × 2 = 8 combinations arise.
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