हिंदी

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

Advertisements
Advertisements

प्रश्न

Write the following compound statement symbolically.

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

योग
Advertisements

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.

shaalaa.com
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 1: Mathematical Logic - Exercise 1.1 [पृष्ठ ७]

वीडियो ट्यूटोरियलVIEW ALL [2]

संबंधित प्रश्न

Using truth table, prove that ~ p ∧ q ≡ (p ∨ q) ∧ ~ p


Write converse, inverse contrapositive of the statement "If two triangles are not congruent then their areas are not equal.


Construct the truth table of the following statement pattern.

[(p → q) ∧ q] → p


Construct the truth table of the following statement pattern.

∼ p ∧ [(p ∨ ∼ q) ∧ q]


Construct the truth table of the following statement pattern.

(q → p) ∨ (∼ p ↔ q)


Construct the truth table of the following:

p → (q → p)


Construct the truth table of the following:

[(∼p ∨ q) ∧ (q → r)] → (p → r)


Express the following statement in symbolic form.

e is a vowel or 2 + 3 = 5


Express the following statement in symbolic form.

Mango is a fruit but potato is a vegetable.


Express the following statement in symbolic form.

Milk is white or grass is green.


Express the following statement in symbolic form.

I like playing but not singing.


Write the truth value of the following statement.

A quadratic equation has two distinct roots or 6 has three prime factors.


Write the negation of the following statement.

It is false that Nagpur is capital of Maharashtra


Write the truth value of the negation of the following statement.

`sqrt5` is an irrational number.


Write the following statement in symbolic form.

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


Find the truth value of the following statement.

Neither 27 is a prime number nor divisible by 4.


If p and q are true and r and s are false, find the truth value of the following compound statement.

p ∧ (q ∧ r)


If p and q are true and r and s are false, find the truth value of the following compound statement.

(p → q) ↔ ~(p ∨ q)


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.

q ∧ ~ p


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.

Even though it is not cloudy, it is still raining.


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.


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


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.

Kanchanganga is in India and Everest is in Nepal.


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 or stocks are not rising iff stocks are rising.


Write the negation of the following statement.

7 is prime number and Tajmahal is in Agra.


Write the negation of the following statement.

10 > 5 and 3 < 8


Negation of p → (p ˅ ∼ q) is ______


If p → q is an implication, then the implication ∼ q → ∼ p is called its


Write the following statement in symbolic form:

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


Negation of “Some men are animal” is ______.


Write the negation of the statement “An angle is a right angle if and only if it is of measure 90°”


If (p ∧ ~ r) → (~ p ∨ q) is a false statement, then respective truth values of p, q and r are ______.


Given 'p' and 'q' as true and 'r' as false, the truth values of p v (q ∧ ~r) and (p → r) ∧ q are respectively


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


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 inverse of the statement "If its quality is good. then it is expensive.", is ______ 


The negation of ∼s ∨ (∼r ∧ s) is equivalent to ______


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


Write the following statement in symbolic form.

It is not true that `sqrt(2)` is a rational number.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×