If p and q are two statements given by
p :30 is a multiple of 5.
q :30 is a multiple of 8.
Write the compound statement by using the connective 'and' check its validity.

Find the component statement of the following compound statements and check whether they are true or false.
100 is divisible by 3,11 and 5.

Write down the converse of the following statements.
If S is a cyclic quadrilateral, then the opposite angles of S are supplementary.

For the following compound statement, first identify the connecting words and then break into component statement.
Write the contrapositive and converse of the statement 'Something is cold implies that it has low temperature'.

Write the negation of the following statements.
If 2 + 3 = 5, then 5 is an odd number.

Find the conditional statement of 'You will get a sweet dish after the dinner'.

Rewrite the following statements in the form of conditional statements
A necessary condition for Indian team to win a cricket match is that the selection committee selects an all-rounder.

Write the negation of the following statements:
(i) Every natural number is greater than 0.
(ii) The sum of 4 and 6 is 10.
(iii) A whole number is an integer.

For each of the following compound statements first identify the connecting words and then break it into component statements.
(i) The sun is cold and the moon rotates around the earth.
(ii)The school works or a holiday is declared.
(iii) Ankita is rich or happy

Given below are two statements
p: 25 is a multiple of 5
q: 25 is a multiple of 8
Write the compound statements connecting these two statements with "and" and "or". In both cases check the validity of the compound statement.

Write the component statements of the following compound statement and check whether the compound statement is true or false
The sun is a star or Sun is plant

Write down the negation
\(\triangle ABC\) is isosceles, if and only if \(\angle B=\angle C\)

For each of the following compound statement first identify the connecting words and then break it into component statements.
(i) All rational numbers are real and all real numbers are not complex.
(ii) Square of an integer is positive or negative.
(iii) The sand heats up quickly in the sun and does not cool down fast at night.
(iv) x = 2 and x = 3 are the roots of the equation 3x² - x - 10 = 0.

State the converse and contrapositive of each of the following statements:
(i) p: A positive integer is prime only if it has
no divisors other then 1 and itself.
(ii) q: I goto a beach whenever it is a sunny day.
(iii) r: if it is not outside, then you feel thirsty.

Check the validity of the statements given below by the method given against it
(i) p: The sum of an irrational number and a rational number is irrational (by contradiction method)
(ii) q: If n is a real number with n > 3, then n² > 9 (by contradiction method)