English

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

Advertisements
Advertisements

Question

Write the following compound statement symbolically.

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

Sum
Advertisements

Solution

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.

shaalaa.com
  Is there an error in this question or solution?
Chapter 1: Mathematical Logic - Exercise 1.1 [Page 7]

RELATED QUESTIONS

Using truth table, prove the following logical equivalence:

(p ∧ q) → r ≡ p → (q → r)


Evaluate: ∫ x . log x dx


Construct the truth table of the following statement pattern.

p → [∼ (q ∧ r)]


If p ∧ q is false and p ∨ q is true, then ______ is not true.


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


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.

e is a vowel or 2 + 3 = 5


Write the truth value of the following statement.

The Himalayas are the highest mountains but they are part of India in the North East.


Write the negation of the following statement.

All men are animals.


Write the following statement in symbolic form.

If triangle is equilateral then it is equiangular.


Find the truth value of the following statement.

It is not true that 3 − 7i is a real number.


Find the truth value of the following statement.

3 is a prime number and an odd number.


Assuming that the following statement is true,

p : Sunday is holiday,

q : Ram does not study on holiday,

find the truth values of the following statements.

Sunday is not holiday or Ram studies on holiday.


Assuming that the following statement is true,

p : Sunday is holiday,

q : Ram does not study on holiday,

find the truth values of the following statements.

Sunday is a holiday and Ram studies on holiday.


If p : He swims

q : Water is warm

Give the verbal statement for the following symbolic statement:

p ↔ ~ q


If p : He swims

q : Water is warm

Give the verbal statement for the following symbolic statement.

~ (p ∨ q)


Fill in the blanks :

Conjunction of two statement p and q is symbolically written as ______.


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

To be brave is necessary and sufficient condition to climb the Mount Everest.


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.


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

If the question paper is not easy then we shall not pass.


If p : Proof is lengthy.
q : It is interesting.
Express the following statement in symbolic form.

Proof is lengthy and it is not interesting.


If p : Proof is lengthy.
q : It is interesting.
Express the following statement in symbolic form.

It is not true that the proof is lengthy but it is interesting.


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 the connective ‘If ... then’.

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


Find the negation of 10 + 20 = 30


Without using truth table prove that:

~ (p ∨ q) ∨ (~ p ∧ q) ≡ ~ p


Write the following statements in symbolic form

Even though it is not cloudy, it is still raining


Choose the correct alternative:

A biconditional statement is the conjunction of two ______ statements


State whether the following statement is True or False:

The converse of inverse of ~ p → q is q → ~ p


If p, q are true statement and r is false statement, then which of the following statements is a true statement.


The symbolic form of the following circuit is (where p, q represents switches S1 and S2 closed respectively)


Which of the following is false?


If p and q are true and rands are false statements, then which of the following is true?


The negation of (p ∨ ∼q) ∧ q is ______


The Boolean expression ∼(q ⇒ ∼p) is equivalent to: ______


The statement, 'If I go to school, then I will get knowledge' is equivalent to ______ 


Conditional of p → q is equivalent to p → ∼ q.


Which of the following is logically equivalent to `∼(∼p \implies q)`?


If p : A man is happy, q : A man is rich, then the symbolic form of ‘A man is neither happy nor rich is ______.


The statement ∼(p ↔ ∼q) is ______.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×