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महाराष्ट्र राज्य शिक्षण मंडळएचएससी वाणिज्य (इंग्रजी माध्यम) इयत्ता १२ वी

State whether the following statement is True or False: p → q is equivalent to p → ~ q - Mathematics and Statistics

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प्रश्न

State whether the following statement is True or False:

p → q is equivalent to p → ~ q

पर्याय

  • True

  • False

MCQ
चूक किंवा बरोबर
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उत्तर

False

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  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 1.1: Mathematical Logic - Q.2

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.


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.

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 value of the following.

Milk is white if and only if sky is blue.


Write the truth values of the following.

24 is a composite number or 17 is a prime number.


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 → s)


If p ∧ q is F, p → q is F then the truth values of p and q are ________.


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.

Please grant me a loan.


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.

Can you speak in English?


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 ______.


Fill in the blanks :

Truth value of if x = 2, then x2 = − 4 is –––––––––.


State whether the following statement is True or False :

Dual of (p ∧ ∼ q) ∨ t is (p ∨ ∼ q) ∨ C.


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.
(2 + 1)2 = 9.


Solve the following :

State which of the following sentences are statements in logic.
The square of any odd number is even.


Solve the following :

State which of the following sentences are statements in logic.
All integers are natural numbers.


Which of the following sentence is a statement? In case of a statement, write down the truth value.

Please carry out my instruction.


Which of the following sentence is a statement? In case of a statement, write down the truth value.

(x − 2) (x − 3) = x2 − 5x + 6 for all x∈R.


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.


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

p ↔ (q → ∼ p)


State the truth value of `sqrt(3)` is not an irrational number


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

~ p ∧ (q ∨ ~ r)


Using truth table prove that p ˅ (q ˄ r) ≡ (p ˅ q) ˄ (p ˅ r).


Which of the following quantified statement is true?


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