Mathematical Reasoning MATHS - Mathematical Reasoning

The negation of the statement.

“7 is greater than 8” is.

1. 7 is equal to 8.
2. 7 is not greater than 8.
3. 8 is less than 7.
4. none of these.

Which of the following statement is a conjunction?

1. Ram and Shyam are friends.
2. Both Ram and Shyam are tall.
3. Both Ram and Shyam are enemies.
4. None of the above.

The converse of the statement.

“If sun is not shining, then sky is filled with clouds” is.

1. If sky is filled with clouds, then the sun is not shining.
2. If sun is shining, then sky is filled with clouds.
3. If sky is clear, then sun is shining.
4. If sun is not shining, then sky is not filled with clouds.

The connective in the statement.

“Earth revolves round the Sun and Moon is a satellite of earth” is.

1. or.
2. Earth.
3. Sun.
4. and.

The negation of the statement.

“Plants take in CO₂ and give out O₂ ” is.

1. Plants do not take in CO₂ and do not give out O₂.
2. Plants do not take in CO₂ or do not give out O₂.
3. Plants take in CO₂ and do not give out O₂ .
4. Plants take in CO₂ or do not give out O₂.

Form the biconditional statement p ↔ q, where.
p: The unit digit of an integer is zero.
q: It is divisible by 5.

Write down the negation of following compound statement:
35 is a prime number or a composite number.

Identify the Quantifiers in the following statement:
There exists a even prime number other than 2.

Find the component statements of the following compound statements.
Chandigarh is the Capital of Haryana and U.P.

Prove by direct method that for any real numbers x, y if x = y, then x² = y².

Using contrapositive method prove that if n 2 is an even integer, then n is also an even integers.

State whether the following sentences are statements are not:

1. The angles opposite to equal sides of a triangle are equal.
2. The moon is a satellite of earth.
3. May God bless you!
4. Asia is a continent.
5. How are you?

Prove by direct method that for any integer ‘n’, n³ - n is always even.
[Hint: Two cases (i) n is even, (ii) n is odd.]

Write the component statements of the following compound statements and check whether the compound statement is true or false.
2 is an even number and a prime number.

Write the component statements of the following compound statements and check whether the compound statement is true or false.
24 is a multiple of 4 and 6.

Check the validity of the following statement.
p : 125 is divisible by 5 and 7.

Prove the following statement by contradication method.
p: The sum of an irrational number and a rational number is irrational.

Write the component statements of the following compound statements and check whether the compound statement is true or false.
All living things have two eyes and two legs.