Which of the following statement is a tautology?

Question

Which of the following statement is a tautology? (A) ((∼ q) ∧ p) ∧ q (B) ((∼ q ) ∧ p ) ∧( p ∧(∼ p )) (C) ((∼ q ) ∧ p ) ∨( p ∨(∼ p )) (D) ( p ∧ q ) ∧(∼( p ∧ q ))

Tardigrade Admin · Accepted Answer

( A )(∼ q ∧ p ) ∧ q =(∼ q ∧ q ) ∧ p = f (B) (∼ q ∧ p ) ∧( p ∧ ∼ p )=∼ q ∧( p ∧ ∼ p )= f (C) (∼ q ∧ p ) ∨( p ∨ ∼ p )=(∼ q ∧ p ) ∨( t )= t (D) ( p ∧ q ) ∧(∼( p ∧ q ))= f

Q. Which of the following statement is a tautology?

$((\sim q) \land p) \land q$

$((\sim q) \land p) \land (p \land (\sim p))$

$((\sim q) \land p) \lor (p \lor (\sim p))$

$(p \land q) \land (\sim (p \land q))$

$(A) (\sim q \land p) \land q = (\sim q \land q) \land p = f$
(B) $(\sim q \land p) \land (p \land \sim p) =\sim q \land (p \land \sim p) = f$
(C) $(\sim q \land p) \lor (p \lor \sim p) = (\sim q \land p) \lor (t) = t$
(D) $(p \land q) \land (\sim (p \land q)) = f$

Q. Which of the following statement is a tautology?

((∼q)∧p)∧q

((∼q)∧p)∧(p∧(∼p))

((∼q)∧p)∨(p∨(∼p))

(p∧q)∧(∼(p∧q))

(A)(∼q∧p)∧q=(∼q∧q)∧p=f (B) (∼q∧p)∧(p∧∼p)=∼q∧(p∧∼p)=f (C) (∼q∧p)∨(p∨∼p)=(∼q∧p)∨(t)=t (D) (p∧q)∧(∼(p∧q))=f

$((\sim q) \land p) \land q$

$((\sim q) \land p) \land (p \land (\sim p))$

$((\sim q) \land p) \lor (p \lor (\sim p))$

$(p \land q) \land (\sim (p \land q))$

$(A) (\sim q \land p) \land q = (\sim q \land q) \land p = f$
(B) $(\sim q \land p) \land (p \land \sim p) =\sim q \land (p \land \sim p) = f$
(C) $(\sim q \land p) \lor (p \lor \sim p) = (\sim q \land p) \lor (t) = t$
(D) $(p \land q) \land (\sim (p \land q)) = f$