Advertisements
Advertisements
Question
Construct the truth table for the following statement
(¬p → r) ∧ (p ↔ q)
Solution
p | q | r | ¬p | ¬p → r | (p ↔ q) | (¬p → r) ∧ (p ↔ q) |
T | T | T | F | T | T | T |
T | T | F | F | T | T | T |
T | F | T | F | T | F | F |
T | F | F | F | T | F | F |
F | T | T | T | T | F | F |
F | T | F | T | F | F | F |
F | F | T | T | T | T | T |
F | F | F | T | F | T | F |
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 v 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 or all the angles of a triangle are not equal
Write the following sentences in symbolic form using statement variables p and q.
19 is not a prime number
Determine the truth value of the following statement.
China is in Europe dr `sqrt(3)` is art integer
Which one of the following sentences is a proposition?
What are you doing?
Which one of the following sentences is a proposition?
How tall this mountain is!
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 v q) v ¬q
Prove that q → p ≡ ¬p → ¬q
Check whether the statement p → (q → p) is a tautology or a contradiction without using the truth table
Choose the correct alternative:
Which one is the inverse of the statement (p v q) → (p ∧ q)?
Choose the correct alternative:
Which one is the contrapositive of the statement (p v q) → r?
Choose the correct alternative:
The truth table for (p ∧ q) v ¬q is given below
p | q | (p ∧ q) v ¬q |
T | T | (a) |
T | F | (b) |
F | T | (c) |
F | F | (d) |
Which one of the following is true?
Choose the correct alternative:
In the last column of the truth table for ¬(p v ¬q) the number of final outcomes of the truth value ‘F’ is
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?