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State whether the following statement is True or False: p ↔ q is false when p and q have different truth values - Mathematics and Statistics

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प्रश्न

State whether the following statement is True or False:

p ↔ q is false when p and q have different truth values

विकल्प

  • True

  • False

MCQ
सत्य या असत्य

उत्तर

True

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  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 1.1: Mathematical Logic - Q.2

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: ∃ n ∈ N such that n + 5 > 10.


State which of the following is the statement. Justify. In case of a statement, state its truth value.

x – 3 = 14


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 ∧ r) ∨ (s → ∼ q)] ↔ (p ∧ r)


If A = {3, 5, 7, 9, 11, 12}, determine the truth value of the following.

∀ x ∈ A, 2x + 9 > 14


Write the truth value of the following statement:

∀ n ∈ N, n + 6 > 8.


State which of the following sentence is a statement. Justify your answer if it is a statement. Write down its truth value.

A triangle has ‘n’ sides.


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.

1 ! = 0


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 :

p ↔ q is false when p and q have ––––––––– truth values.


Fill in the blanks :

Let p : the problem is easy. r : It is not challenging then verbal form of ∼ p → r is –––––––––.


Solve the following :

State which of the following sentences are statements in logic.
(2 + 1)2 = 9.


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.


Assuming the following statement.
p : Stock prices are high.
q : Stocks are rising.
to be true, find the truth value of the following.

It is false that stocks are rising and stock prices are high.


If p, q, r are statements with truth values T, T, F respectively determine the truth values of the following.

p ↔ (q → ∼ p)


If statements p, q are true and r, s are false, determine the truth values of the following.

~ p ∧ (q ∨ ~ r)


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