Quiz on Logics and Proofs

The compound propositions p and q are called logically equivalent if ________ is a tautology.

• p ↔ q

• p → q

• ¬ (p ∨ q)

• ¬ p ∨ ¬ q

p → q is logically equivalent to:

• ¬p ∨ ¬q

• p ∨ ¬q

• ¬p ∨ q

• ¬p ∧ q

p ∨ q is logically equivalent to:

• ¬q → ¬p

• q → p

• ¬p → ¬q

• ¬p → q

Which of the following statement is a proposition?

• Get me a glass of milkshake

• God bless you!

• What is the time now?

• The only odd prime number is 2

Let P: If Sahil bowls, Saurabh hits a century. , Q: If Rajubowls,Sahil gets out on first ball. Now if P is true and Q is false then which of the following can be true?

• Raju bowled and Sahil got out on first ball

• Raju did not bowled

• Sahil bowled and Saurabh hits a century

• Sahil bowled and Saurabh got out

Let P: We should be honest, Q: We should be dedicated. R: We should be overconfident. Then 'We should be honest or dedicated but not overconfident.' is best represented by:

• P V ¬Q V R

• (P ∧ ¬Q)∧ R

• (P V Q)∧ R

• (P V Q)∧ ¬R

¬ (p ∨ q) ∧ (p ∧ q) is a ___________

• Tautology

• Contradiction

• Contingency

• None of the mentioned

(p ∨ ¬ p) ∨ (q ∨ T) is a __________

• Tautology

• Contradiction

• Contingency

• None of the mentioned

What are the contrapositive of the conditional statement "I come to class whenever there is going to be a test.

• "If I come to class, then there will be a test."

• "If I do not come to class, then there will not be a test."

• "If there is not going to be a test, then I don't come to class."

• "If there is going to be a test, then I don't come to class."

Which rule of inference is used in each of these arguments, "If it is Wednesday, then the Smartmart will be crowded. It is Wednesday. Thus, the Smartmart is crowded."

• Modus tollens

• Modus ponens

• Disjunctive syllogism

• Simplification