Advertisements
Advertisements
प्रश्न
Write the truth value of the following.
Milk is white if and only if sky is blue.
Advertisements
उत्तर
Let p: Milk is white.
q: Sky is blue
Then the symbolic form of the given statement is p↔q.
The truth values of both p and q are T.
∴ The truth value of p↔q is T .......[T↔T ≡ T]
APPEARS IN
संबंधित प्रश्न
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 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.
Zero is a complex number.
State which of the following is the statement. Justify. In case of a statement, state its truth value.
Congruent triangles are similar.
State which of the following is the statement. Justify. In case of a statement, state its truth value.
All real numbers are whole numbers.
State which of the following is the statement. Justify. In case of a statement, state its truth value.
It rains heavily.
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
`sqrt5` is an irrational but `3sqrt5` is a complex number.
Write the truth value of the following statement:
∀ n ∈ N, n2 + n is even number while n2 – n is an odd 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.
1 is a 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 π 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 - y2 = (x + y)(x - y) 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.
The number of arrangements of 7 girls in a row for a photograph is 7!.
State which of the following sentence is a statement. Justify your answer if it is a statement. Write down its truth value.
Give me a compass box.
State which of the following sentence is a statement. Justify your answer if it is a statement. Write down its truth value.
If a + b < 7, where a ≥ 0 and b ≥ 0 then a < 7 and b < 7.
Choose the correct alternative :
Which of the following is an open statement?
If p and q are two statements then (p → q) ↔ (∼ q → ∼ p) is ______.
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.
State whether the following statement is True or False :
“His birthday is on 29th February” is not a statement.
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.
x + 3 = 8 ; x is variable.
Solve the following :
State which of the following sentences are statements in logic.
z is a positive number.
Solve the following :
State which of the following sentences are statements in logic.
(a + b)2 = a2 + 2ab + b2 for all a, b ∈ R.
Solve the following :
State which of the following sentences are statements in logic.
Do not come inside the room.
Which of the following sentence is a statement? In case of a statement, write down the truth value.
Every parallelogram is a rhombus.
Which of the following sentence is a statement? In case of a statement, write down the truth value.
Please carry out my instruction.
If p, q, r are statements with truth values T, T, F respectively determine the truth values of the following.
(p ∧ q) → ∼ p.
If p, q, r are statements with truth values T, T, F respectively determine the truth values of the following.
p ↔ (q → ∼ p)
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, x2 < 18.
Choose the correct alternative :
Which of the following statement is true?
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:
The dual of (p ˄ q) ˅ ~ q is (p ˅ q) ˄ ~ q
Which of the following quantified statement is true?
Let a: ~ (p ∧ ~ r) v (~ q v s) and
b: (p v s) ↔ (q ∧ r).
If the truth values of p and q are true and that of rands are false, then the truth values of a and bare respectively.
If (p ∧ ~ q) → ~ p is false, the truth values of p and q are respectively.
Find the truth value of the following compound statement:
5 + 4 = 9 and 6 × 3 = 12
