Given below are two statements
p :100 is a multiple of 5.
q :100 is a multiple of 4.
Write the compound statement connecting these two statements with 'and' and check its validity.

Check the validity of the following statements
p :20 is a multiple of 4 and 5.

By giving a counter example, show that the following statement is false. If x is even integer, then x is a prime.

Using contrapositive method, prove that if n² is an even integer, then n is also an even integer.

Identify the component statements and the connecting word in in the following compound statements.
(i) It is raining or the Sun is shining|
(ii) All primes are either even or odd
(iii) Two lines intersect at a point or they are parallel.

For each of the following statement,determine whether an inclusive 'OR' or exclusive 'OR' is used.Give reason for your answer
A lady gives birth to a baby boy or a baby girl

Write the negation of the following statements and check whether the resulting statements are true.
(i) The sum of 2 and 3 is 4.
(ii) \(\sqrt { 3 } \) is rational
(iii) New Delhi is a city.
(iv) Every natural number is greater than 0

Write down the compound statements by using 'and','or' of the following statements
p: Mohan is honest      
q: Mohan is qualified

Rewrite the following statements in the form of conditional statements
Mohan will be a good student if he studies hard.

Write the component statements of the following compound statement and check whether the compound statement is true or false
Every rectangle is a square and every square is a rectangle

Verify by method of contradiction p:\(\sqrt { 11 } \) is irrational.

Write down the negation
2 + 4 > 5 or 3 + 4 < 6.

Give three examples of sentences which are not statements. Give reasons for the answers.

Show that the statement
p:"If x is a real number such that :x³+ 4x = 0 then x is 0" is true by
(i) direct method
(ii) method of contradiction
(iii) method of contrapositive.

Which of the following statements are true and which are false? In each case give a valid reason for saying so.
(i) p: Each radius of a circle is a chord of the circle.
(ii) q: The centre of a circle bisects each chord of the circle.
(iii) r: Circle is a particular case of an ellipse.
(iv) s: If x and y are integers such that x > y then -x< -y.
(v) t: \(\sqrt { 11 } \)is a rational number.