Advertisements
Advertisements
Question
If the statement p, q are true statement and r, s are false statement then determine the truth value of the following:
(p → q) ∧ ∼ r
Solution
Truth values of p and q are T and truth values of r and s are F.
(p → q) ∧ (∼ r) ≡ (T → T) ∧ (∼ F)
≡ T ∧ T ≡ T
Hence the truth value of the given statement is true.
APPEARS IN
RELATED QUESTIONS
If p ˄ q = F, p → q = F, then the truth value of p and q is ______.
Write truth values of the following statements :`sqrt5` is an irrational number but 3 +`sqrt 5` is a complex number.
Write truth values of the following statements: ∃ n ∈ N such that n + 5 > 10.
Write the following statement in symbolic form and find its truth value:
∀ n ∈ N, n2 + n is an even number and n2 - n is an odd number.
If p, q, r are the statements with truth values T, F, T, respectively then find the truth value of (r ∧ q) ↔ ∼ p
State which of the following is the statement. Justify. In case of a statement, state its truth value.
5 + 4 = 13
State which of the following is the statement. Justify. In case of a statement, state its truth value.
Please get me breakfast.
State which of the following is the statement. Justify. In case of a statement, state its truth value.
x2 = x
State which of the following is the statement. Justify. In case of a statement, state its truth value.
Do you like Mathematics?
State which of the following is the statement. Justify. In case of a statement, state its truth value.
x2 – 6x – 7 = 0, when x = 7
State which of the following is the statement. Justify. In case of a statement, state its truth value.
It rains heavily.
Write the truth values of the following.
5 is a prime number and 7 divides 94.
Write the truth values of the following.
It is not true that 5−3i is a real number.
Write the truth value of the following.
Milk is white if and only if sky is blue.
If the statement p, q are true statement and r, s are false statement then determine the truth value of the following:
[∼ p ∧ (∼ q ∧ r)] ∨ [(q ∧ r) ∨ (p ∧ r)]
If the statement p, q are true statement and r, s are false statement then determine the truth value of the following:
[(∼ p ∧ q) ∧ ∼ r] ∨ [(q → p) → (∼ s ∨ r)]
If the statement p, q are true statement and r, s are false statement then determine the truth value of the following:
∼ [(∼ p ∧ r) ∨ (s → ∼ q)] ↔ (p ∧ r)
If A = {3, 5, 7, 9, 11, 12}, determine the truth value of the following.
∃ x ∈ A such that x2 < 0
If A = {3, 5, 7, 9, 11, 12}, determine the truth value of the following.
∀ x ∈ A, x is an even number.
If p ∧ q is F, p → q is F then the truth values of p and q are ________.
If A = {1, 2, 3, 4, 5} then which of the following is not true?
`sqrt5` is an irrational but `3sqrt5` is a complex number.
Write the truth value of the following statement:
The square of any even number is odd or the cube of any odd number is odd.
State which of the following sentence is a statement. Justify your answer if it is a statement. Write down its truth value.
You are amazing!
State which of the following sentence is a statement. Justify your answer if it is a statement. Write down its truth value.
`sqrt(-4)` is an irrational number.
State which of the following sentence is a statement. Justify your answer if it is a statement. Write down its truth value.
x2 − 6x + 8 = 0 implies x = −4 or x = −2.
State which of the following sentence is a statement. Justify your answer if it is a statement. Write down its truth value.
He is an actor.
State which of the following sentence is a statement. Justify your answer if it is a statement. Write down its truth value.
(x + y)2 = x2 + 2xy + y2 for all x, y ∈ R.
State which of the following sentence is a statement. Justify your answer if it is a statement. Write down its truth value.
Every real number is a complex number.
State which of the following sentence is a statement. Justify your answer if it is a statement. Write down its truth value.
The number 2 is the only even prime number.
State which of the following sentence is a statement. Justify your answer if it is a statement. Write down its truth value.
The number of arrangements of 7 girls in a row for a photograph is 7!.
Choose the correct alternative :
Which of the following is an open statement?
The negation of the proposition “If 2 is prime, then 3 is odd”, is ______
Choose the correct alternative :
The statement (∼ p ∧ q) ∨∼ q is
Choose the correct alternative:
Which of the following is always true?
Choose the correct alternative :
Conditional p → q is equivalent to
Fill in the blanks :
The statement q → p is called as the ––––––––– of the statement p → q.
If p ∨ q is true then truth value of ∼ p ∨ ∼ q is ______.
State whether the following statement is True or False :
There are 24 months in year is a statement.
State whether the following statement is True or False :
Dual of “John and Ayub went to the forest” is “John and Ayub went to the forest”.
State whether the following statement is True or False :
x2 = 25 is true statement.
Solve the following :
State which of the following sentences are statements in logic.
Ice cream Sundaes are my favourite.
Solve the following :
State which of the following sentences are statements in logic.
Read a lot to improve your writing skill.
Solve the following :
State which of the following sentences are statements in logic.
(2 + 1)2 = 9.
Solve the following :
State which of the following sentences are statements in logic.
If x is real number then x2 ≥ 0.
Which of the following sentence is a statement? In case of a statement, write down the truth value.
a2 − b2 = (a + b) (a − b) for all a, b ∈ R.
Which of the following sentence is a statement? In case of a statement, write down the truth value.
What are the causes of rural unemployment?
Which of the following sentence is a statement? In case of a statement, write down the truth value.
0! = 1
Which of the following sentence is a statement? In case of a statement, write down the truth value.
The quadratic equation ax2 + bx + c = 0 (a ≠ 0) always has two real roots.
Determine the truth value of the following statement.
x + y = 0 is the equation of a straight line if and only if y2 = 4x is the equation of the parabola.
Assuming the following statement.
p : Stock prices are high.
q : Stocks are rising.
to be true, find the truth value of the following.
If stock prices are high then stocks are not rising.
If p, q, r are statements with truth values T, T, F respectively determine the truth values of the following.
∼ (p ∧ q) → ∼ (q ∧ p)
If A = {2, 3, 4, 5, 6, 7, 8}, determine the truth value of the following statement.
∃ x ∈ A, such that x + 3 < 11.
If p is any statement then ( p ˅ ∼ p) is a
State the truth value of `sqrt(3)` is not an irrational number
State the truth value of (p ˄ ∼p)
The dual of the statement (p ˅ q) ˄ (r ˅ s) is ______.
State whether the following statement is True or False:
p → q is equivalent to p → ~ q
State whether the following statement is True or False:
Truth value of `sqrt(3)` is not an irrational number is F
State whether the following statement is True or False:
(p ˅ q) ˄ ~ p is a contradiction
State whether the following statement is True or False:
Mathematical identities are true statements
The truth value of negation of “London is in England” is ______
The negation of 'For every real number x, `x^2 ≥ 0`' is ______
If p ↔ (~ p → q) is false, then the truth values of p and q are respectively ______.
If p `rightarrow` (p ∧ ∼q) is false, then the truth values of p and q are respectively ______.
Using truth table prove that:
`p → (q ∨ r) ≡ (p → q) ∨ (p → r)`
Find the truth value of the following compound statement:
5 + 4 = 9 and 6 × 3 = 12