Logical Connectives
Trending Questions
Q. The following statement (p→q)→[(∼p→q)→q] is:
- a tautology
- equivalent to ∼p→q
- equivalent to p→∼q
- a fallacy
Q. Which of the following biconditional statements are true?
- 2≠3 ↔ 2>3 or 2<3
- 2=3 ↔ 3=4
- a <3 ↔ a>3
- a=3 ↔ a ≤ 3 and a ≥ 3
Q. If a then b and if b then c ⟹ If a then c.
- False
- True
Q. The boolean expression ((p∧q)∨(p∨∼q))∧(∼p∧∼q) is equivalent to:
- p∧(∼q)
- (∼p)∧(∼q)
- p∨(∼q)
- p∧q
Q. The logical statement (p⇒q)∧(q⇒∼p) is equivalent to
- ∼p
- p
- q
- ∼q
Q. If the Boolean expression (p ⊕ q) ∧ (∼ p ⊙ q) is equivalent to p ∧ q, where ⊕, ⊙∈{∧, ∨}, then the ordered pair (⊕, ⊙) is:
- (∨, ∨)
- (∨, ∧)
- (∧, ∧)
- (∧, ∨)
Q. If the truth value of the statement p→(∼q∨r) is false(F), then the truth values of the statements p, q, r are respectively :
- T, T, F
- T, F, T
- T, F, F
- F, T, T
Q. The inverse of the proposition (p∧∼q)→r is
- ∼r→(∼p∨q)
- (∼p∨q)→∼r
- ∼p→(p∧r)
- r→(p ∧∼q)
Q.
The dual of statement p∨(q∧r)≡(p∨q)∧(p∨r) is
p∧(q∨r)≡(p∧q)∨(p∧r)
p∨(q∧r)≡(p∧q)∧r
p∧(q∧r)≡(p∧q)∧r
p∨(q∨r)=(p∧q)∧r
Q. Let p, q, r denote the arbitary statements then the logical equivalance of the statement p⇒(q∨r) is
- (p∨q)⇒r
- (p⇒∼q)∧(p⇒r)
- (p⇒q)∧(p⇒∼r)
- (p⇒q)∨(p⇒r)