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महाराष्ट्र राज्य शिक्षण मंडळएचएससी विज्ञान (सामान्य) इयत्ता १२ वी

Write the following compound statement symbolically. If ΔABC is right-angled at B, then m∠A + m∠C = 90°. - Mathematics and Statistics

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प्रश्न

Write the following compound statement symbolically.

If ΔABC is right-angled at B, then m∠A + m∠C = 90°.

बेरीज
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उत्तर

Let p: ΔABC is right-angled at B.

Let q: m∠A + m∠C = 90°

Then the symbolic form of the given statement is p → q.

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पाठ 1: Mathematical Logic - Exercise 1.1 [पृष्ठ ७]

व्हिडिओ ट्यूटोरियलVIEW ALL [3]

संबंधित प्रश्‍न

Examine whether each of the following statement patterns is a tautology or a contradiction or a contingency.

[~(~p ∧ ~q)] v q


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(A) A triangle is equilateral if and only if it is equiangular.
(B) Price increases and demand falls


Write the following compound statement symbolically. 

Hima Das wins gold medal if and only if she runs fast.


Construct the truth table of the following statement pattern.

(p ∧ ∼q) ↔ (p → q)


Construct the truth table of the following statement pattern.

p → [∼ (q ∧ r)]


Construct the truth table of the following:

p → (q → p)


Construct the truth table of the following:

(∼p ∨ ∼q) ↔ [∼(p ∧ q)]


Construct the truth table of the following:

[(∼p ∨ q) ∧ (q → r)] → (p → r)


Determine the truth values of p and q in the following case:

(p ∨ q) is T and (p ∧ q) is T


Determine the truth values of p and q in the following case:

(p ∧ q) is F and (p ∧ q) → q is T


Express the following statement in symbolic form.

I like playing but not singing.


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Even though it is cloudy, it is still raining.


Write the truth value of the following statement.

Earth is a planet and Moon is a star.


Write the negation of the following statement.

2 + 3 ≠ 5


Write the following statement in symbolic form.

If triangle is equilateral then it is equiangular.


Write the following statement in symbolic form.

If Kutub-Minar is in Delhi then Taj-Mahal is in Agra.


If p : He swims

q : Water is warm

Give the verbal statement for the following symbolic statement.

q → p


If p : He swims

q : Water is warm

Give the verbal statement for the following symbolic statement.

q ∧ ~ p


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If Kiran drives the car, then Sameer will walk.


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Assuming the first statement p and second as q. Write the following statement in symbolic form.

It is not true that Ram is tall and handsome.


Let p : Sachin wins the match.
q : Sachin is a member of Rajya Sabha.
r : Sachin is happy.
Write the verbal statement of the following.
p→(q ∨ r)


Let p : Sachin wins the match.
q : Sachin is a member of Rajya Sabha.
r : Sachin is happy.
Write the verbal statement of the following.

(p ∧ q) ∧ ∼ r


Rewrite the following statement without using conditional –
(Hint : p → q ≡ ∼ p ∨ q)

If demand falls, then price does not increase.


Write the negation of the following.

An angle is a right angle if and only if it is of measure 90°.


Write the negation of the following.

If x ∈ A ∩ B, then x ∈ A and x ∈ B.


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p : Stock prices are high.

q : Stocks are rising.

to be true, find the truth value of the following.

Stock prices are high or stocks are not rising iff stocks are rising.


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If a quadrilateral is rhombus then it is not a square.


Write the negation of the following statement.

10 > 5 and 3 < 8


Write the negation of the following statement.

I will have tea or coffee.


Negation of p → (p ˅ ∼ q) is ______


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The negation of the statement (p ˄ q) `→` (r ˅ ∼ p) is ______.


Find the negation of 10 + 20 = 30


Write the following statement in symbolic form:

Milk is white if and only if the sky is not blue.


Without using truth table show that -

(p ˅ q) ˄ (∼p v ∼q) ≡ (p ∧ ∼q) ˄ (∼p ∧ q)


Negation of “Some men are animal” is ______.


The negation of the statement: "Getting above 95% marks is a necessary condition for Hema to get admission in good college'' is ______


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The statement ∼(p ↔ ∼q) is ______.


Write the contrapositive of the inverse of the statement:

‘If two numbers are not equal, then their squares are not equal’.


Write the negation of (p `leftrightarrow` q).


Using truth table prove that:

~ (p `leftrightarrow` q) ≡ (p ∧ ~ q) ∨ (q ∧ ~ p)


Construct the truth table for the statement pattern:

[(p → q) ∧ q] → p


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