Question

Write which of the following statements are true? Justify your answer.
(i) The set of all integers is contained in the set of all rational numbers.
(ii) The set of all crows is contained in the set of all birds.
(iii) The set of all rectangles is contained in the set of all squares.
(iv) The sets P = {a} and B = {{a}} are equal.
(v) The sets A={x: x is a letter of word “LITTLE”} AND, b = {x: x is a letter of the word “TITLE”} are equal.

Answer 1

(i) True

Since, a rational number is represented by the form p/q where p and q are integers and (q not equal to 0) keeping q = 1 we can place any number as p. Which then will be an integer.

(ii) True

Crows are also birds, Therefore, they are contained in the set of all birds.

(iii) False

Since, very square can be a rectangle, but every rectangle cannot be a square.

(iv) False

P = {a}

B = {{a}}

But {a} = P

B = {P}

Thus, they are not equal.

(v) True

A = For the “LITTLE”

A = {L, I, T, E} = {E, I, L, T}

B = For the “TITLE”

B = {T, I, L, E} = {E, I, L, T}

∴ A = B