Mathematical Reasoning - Online Test
Q1. Let p and q be two propositions. Then the inverse of the implication p→q is
Answer : Option D
Explaination / Solution:
inverse of p→q≡∼p→∼q
Q2. Let p and q be two propositions. Then the contrapositive of the implication p→q is
Answer : Option A
Explaination / Solution:
The contrapositive of p→q≡∼q→∼p
Q3. Let p and q be two propositions. Then the implication p→q is false ,when
Answer : Option C
Explaination / Solution:
Since T →F≡F
Q4. Let p and q be two propositions. Then the implication p↔∼q is true ,when
Answer : Option C
Explaination / Solution:
| p | q | ||
| T | T | F | F |
| T | F | T | T |
| F | T | F | T |
| F | F | T | F |
Q5. For any three propositions p , q , and r , the proposition (p∧q)∧(q∧r) is true , when
Answer : Option C
Explaination / Solution:
hence p=T , q=T, r=T
Q6. Let p and q be two propositions. Then the implication ∼(p↔q) is :
Answer : Option D
Explaination / Solution:
∼(p↔q)≡(p∧∼q)∨(q∧∼p)
Q7. p∧(q∧r) is logically equivalent to
Answer : Option D
Explaination / Solution:
Associative law
Q8. ∼(∼p)↔p is
Answer : Option A
Explaination / Solution:
Q9. Which of the following is a proposition ?
Answer : Option C
Explaination / Solution:
it is a statement which is F.Hence it is a proposition.Other options are open sentences which are not propositions
Q10. Which of the following proposition is a tautology ?
Answer : Option B
Explaination / Solution:
and Associative law
