Write the negation of the following simple statements

The number 17 is prime.

Violets are blue.

Write down the negation of following compound statements

(i) All rational numbers are real and complex.

(ii) All real numbers are rationals or irrationals.

(iii) x = 2 and x = 3 are roots of the Quadratic equation x² – 5x + 6 = 0.

(iv) A triangle has either 3-sides or 4-sides.

(v) 35 is a prime number or a composite number.

(vi) All prime integers are either even or odd.

(vii) |x| is equal to either x or – x.

(viii) 6 is divisible by 2 and 3.

Split each of the following into simple sentences and determine whether it is true or false. Also, determine whether an ‘inclusive or’ or ‘exclusive or’ is used.

(i) The sum of 3 and 7 is 10 or 11.

(ii) (1 + i) is a real or a complex number.

(iii) Every quadratic equation has one or two real roots.

(iv) You are wet when it rains, or you are in a river.

(v) 24 is a multiple of 5 or 8.

(vi) Every integer is rational or irrational.

(vii) For getting a driving license, you should have a ration card or a passport.

(viii) 100 is a multiple of 6 or 8.

(ix) Square of an integer is positive or negative.

(x) Sun rises or Moon sets.

Find the component statements of the following compound statements:

(i) The sky is blue, and the grass is green.

(ii) The earth is round, or the sun is cold.

(iii) All rational numbers are real, and all real numbers are complex.

(iv) 25 is a multiple of 5 and 8.

Determine whether the following compound statements are true or false:

(i) Delhi is in India and 2 + 2 = 4

(ii) Delhi is in England and 2 + 2 = 4

(iii) Delhi is in India and 2 + 2 = 5

(iv) Delhi is in England and 2 + 2 = 5

Write the negation of the following simple statements

The number 17 is prime.