Advertisements
Advertisements
Question
Show that ¬(p → q) ≡ p ∧¬q
Advertisements
Solution
| p | q | p → q | ¬(p → q) | ¬q | p ∧¬q |
| T | T | T | F | F | F |
| T | F | F | T | T | T |
| F | T | T | F | F | F |
| F | F | T | F | T | F |
The entries in the columns corresponding to ¬(p → q) and p ∧ ¬q are identical and hence they are equivalent.
APPEARS IN
RELATED QUESTIONS
Let p : Jupiter is a planet and q : India is an island be any two simple statements. Give verbal sentence describing the following statement.
¬ P
Let p : Jupiter is a planet and q : India is an island be any two simple statements. Give verbal sentence describing the following statement.
P ∧ ¬q
Let p : Jupiter is a planet and q : India is an island be any two simple statements. Give verbal sentence describing the following statement.
p → ¬q
Write the following sentences in symbolic form using statement variables p and q.
19 is a prime number and all the angles of a triangle are equal
Determine the truth value of the following statement.
If 6 + 2 = 5, then the milk is white.
Determine the truth value of the following statement.
It is not true that 5 + 5 = 9 or Earth is a planet
Determine the truth value of the following statement.
11 is a prime number and all the sides of a rectangle are equal
Write the converse, inverse, and contrapositive of the following implication.
If a quadrilateral is a square then it is a rectangle
Construct the truth table for the following statement.
¬P ∧ ¬q
Construct the truth table for the following statement.
(p v q) v ¬q
Show that (p ∧ q) ≡ ¬p v ¬q
Check whether the statement p → (q → p) is a tautology or a contradiction without using the truth table
Prove p → (q → r) ≡ (p ∧ q) → r without using the truth table
Choose the correct alternative:
Which one of the following statements has the truth value T?
Choose the correct alternative:
Which one is the contrapositive of the statement (p v q) → r?
Choose the correct alternative:
Which one of the following is incorrect? For any two propositions p and q, we have
Choose the correct alternative:
Determine the truth value of each of the following statements:
(a) 4 + 2 = 5 and 6 + 3 = 9
(b) 3 + 2 = 5 and 6 + 1 = 7
(c) 4 + 5 = 9 and 1 + 2 = 4
(d) 3 + 2 = 5 and 4 + 7 = 11
Choose the correct alternative:
Which one of the following is not true?
