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

Choose the correct alternative: Which of the following is always true? - Mathematics and Statistics

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प्रश्न

Choose the correct alternative:

Which of the following is always true?

पर्याय

  • (p → q) ≡ ∼ q → ∼ p

  • ∼ (p ∨ q) ≡ ∼ p ∨ ∼ q

  • ∼ (p → q) ≡ p ∧ ∼ q

  • ∼ (p ∨ q) ≡ ∼ p ∧ ∼ q

  • ∼ (p → q) ≡ p ∧ ∼ q and ∼ (p ∨ q) ≡ ∼ p ∧ ∼ q

MCQ
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उत्तर

∼ (p → q) ≡ p ∧ ∼ q and ∼ (p ∨ q) ≡ ∼ p ∧ ∼ q

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  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 1: Mathematical Logic - Miscellaneous Exercise 1 [पृष्ठ ३०]

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बालभारती Mathematics and Statistics 1 (Commerce) [English] Standard 12 Maharashtra State Board
पाठ 1 Mathematical Logic
Miscellaneous Exercise 1 | Q 1.09 | पृष्ठ ३०

संबंधित प्रश्‍न

Write the truth value of the following.

If 3 × 5 = 8 then 3 + 5 = 15.


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


Which of the following sentence is the statement in logic? Justify. Write down the truth value of the statement:

4! = 24.


Which of the following sentence is the statement in logic? Justify. Write down the truth value of the statement:

If x is a whole number then x + 6 = 0.


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.

It may rain today.


Which of the following is not a statement?


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


State whether the following statement is True or False :

Dual of “John and Ayub went to the forest” is “John and Ayub went to the forest”.


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 :

p ∧ t = p.


Solve the following :

State which of the following sentences are statements in logic.
(a + b)2 = a2 + 2ab + b2 for all a, b ∈ R.


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

The square of every real number is positive.


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.


Determine the truth value of the following statement.

x + y = 0 is the equation of a straight line if and only if y2 = 4x is the equation of the parabola.


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

Stock prices are not high or stocks are rising.


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

Stock prices are high and stocks are rising if and only if stock prices are high.


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.


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 ∧ ∼ q)]


State whether the following statement is True or False:

Mathematical identities are true statements


State whether the following statement is True or False:

p ˅ ~ p ≡ ~ c


If p ↔ q and p → q both are true, then find truth values of the following with the help of activity

p ˄ q

p ↔ q and p → q both are true if p and q has truth value `square`, `square` or `square`, `square`

p ˄ q

i. If both p and q are true, then p ˄ q = `square` ˄ `square` = `square`

ii. If both p and q are false, then p ˄ q = `square` ˄ `square` = `square`


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 : Every square is a rectangle. q : Every rhombus is a kite, then truth values of p `rightarrow` q and p `leftrightarrow` q are ______ and ______ respectively.


Using truth table prove that:

`p → (q ∨ r) ≡ (p → q) ∨ (p → r)`


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