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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

उत्तर

False

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

संबंधित प्रश्‍न

If p, q, r are the statements with truth values T, F, T, respectively then find the truth value of (r ∧ q) ↔ ∼ p


Write the truth values of the following.

It is not true that 5−3i is a real number.


Write the truth value of the following.

Milk is white if and only if sky is blue.


If the statement p, q are true statement and r, s are false statement then determine the truth value of the following:

(q ∧ r) ∨ (∼ p ∧ s)


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.

You are amazing!


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

It may rain today.


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


If p ∨ q is true then truth value of ∼ p ∨ ∼ q 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 ∨ q has truth value F is both p and q has truth value F.


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.
All integers are natural numbers.


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

If stock prices are high then stocks are not rising.


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


State whether the following statement is True or False:

Mathematical identities are true statements


Given following statements
p: 9 × 5 = 45
q: Pune is in Maharashtra
r: 3 is the smallest prime number

Write truth values by activity

i) (p ˄ q) ˄ r = `(square` ˄ `square)` ˄ `square`

= `square` ˄ `square`

= `square`

ii) ~ ( p ˄ r ) = `~(square` ˄ `square)`

= `~ square`

= `square`

iii) p → q = `square → square`

= `square`


If p ↔ (~ p → q) is false, then the truth values of p and q are respectively ______.


If q Λ ∼p is T, then which of the following is correct?


If p `rightarrow` (p ∧ ∼q) is false, then the truth values of p and q are respectively ______.


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