Advertisements
Advertisements
प्रश्न
If p, q, r are the statements with truth values T, F, T, respectively then find the truth value of (r ∧ q) ↔ ∼ p
Advertisements
उत्तर
(r ∧ q) ↔ ∼ p
≡ (T ∧ F) ↔ ∼T
≡(T ∧ F) ↔ F [1]
≡ F ↔ F
≡ T
Hence, the truth value is ‘T’
APPEARS IN
संबंधित प्रश्न
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.
Using truth tables, examine whether the statement pattern (p ∧ q) ∨ (p ∧ r) is a tautology, contradiction or contingency.
State which of the following is the statement. Justify. In case of a statement, state its truth value.
Close the door.
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.
A quadratic equation cannot have more than two roots.
State which of the following is the statement. Justify. In case of a statement, state its truth value.
Do you like Mathematics?
Write the truth values of the following.
5 is a prime number and 7 divides 94.
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
Which of the following sentence is the statement in logic? Justify. Write down the truth value of the statement:
cos2θ − sin2θ = cos2θ for all θ∈R.
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.
Did you eat lunch yet?
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.
1 ! = 0
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 :
For the following three statements
p : 2 is an even number.
q : 2 is a prime number.
r : Sum of two prime numbers is always even.
Then, the symbolic statement (p ∧ q) → ∼ r means.
If p and q are two statements then (p → q) ↔ (∼ q → ∼ p) is ______.
Fill in the blanks :
Truth value of 2 + 3 = 5 if and only if − 3 > − 9 is –––––––––.
State whether the following statement is True or False :
p ∧ t = p.
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.
If x is real number then x2 ≥ 0.
Solve the following :
State which of the following sentences are statements in logic.
What a horrible sight it was!
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?
Determine the truth value of the following statement.
4 + 5 = 7 or 9 − 2 = 5
Determine the truth value of the following statement.
If 9 > 1 then x2 − 2x + 1 = 0 for x = 1
If p, q, r are statements with truth values T, T, F respectively determine the truth values of the following.
(p ∧ ∼ q) ∨ (∼ p ∧ q)
If A = {2, 3, 4, 5, 6, 7, 8}, determine the truth value of the following statement.
∃ x ∈ A, such that 3x + 2 > 9
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
Choose the correct alternative :
Which of the following statement is true?
State whether the following statement is True or False:
The dual of (p ˄ q) ˅ ~ q is (p ˅ q) ˄ ~ q
The truth value of negation of “London is in England” is ______
The truth value of the statement “Neither 27 is a prime number nor divisible by 4” is ______
Without using truth table show that
(p ∨ q) ∧ (~ p ∨ ~ q) ≡ (p ∧ ~ q) ∨ ( ~ p ∧ q)
If p ↔ q and p → q both are true, then find truth values of the following with the help of activity
p ˄ q
|
p ↔ q and p → q both are true if p and q has truth value `square`, `square` or `square`, `square` p ˄ q i. If both p and q are true, then p ˄ q = `square` ˄ `square` = `square` ii. If both p and q are false, then p ˄ q = `square` ˄ `square` = `square` |
Which of the following quantified statement is true?
If the truth value of statement (q ∧ ~ r) → p is false (F), then the truth values of the statements p, q, rare respectively.
If q Λ ∼p is T, then which of the following is correct?
Using truth table prove that:
`p → (q ∨ r) ≡ (p → q) ∨ (p → r)`
