HSC Science (General) १२ वीं कक्षा - Maharashtra State Board Question Bank Solutions for Mathematics and Statistics

Choose the correct alternative :

Which of the following is an open statement?

Which of the following statements is false?

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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.

Choose the correct alternative :

If p : He is intelligent.
q : He is strong
Then, symbolic form of statement “It is wrong that, he is intelligent or strong” is

The negation of the proposition “If 2 is prime, then 3 is odd”, is ______.

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The statement (∼ p ∧ q) ∨∼ q is

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Which of the following is always true?

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∼ (p ∨ q) ∨ (∼ p ∧ q) is logically equivalent to

If p and q are two statements then (p → q) ↔ (∼ q → ∼ p) is ______.

The p.m.f. of a r.v. X is given by P (X = x) =`("" ^5 C_x ) /2^5` , for x = 0, 1, 2, 3, 4, 5 and = 0, otherwise.

Then show that P (X ≤ 2) = P (X ≥ 3).

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If p is the sentence ‘This statement is false’ then

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Conditional p → q is equivalent to

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Negation of the statement “This is false or That is true” is

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 ______.

Fill in the blanks :

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

Fill in the blanks :

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

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

Truth value of 2 + 3 < 6 is F.