Question

State whether true or false. Give reasons to support your answer.
(a) Every subset of an infinite set is infinite.
(b) The set of all rectangles is contained in the set of all squares.
(c) A set can have infinitely many subsets.
(d) For every given data there is a mode of the data values.
(e) The cardinality of the set P({T, R, U, E}) is 4.
(f) {x ∈ N | x
2 − 25 = 0} = {5, −5}.
(g) {q} ∈ {p, q, r}.
(h) The set A = {x | x is a letter of the word ”TRAFFIC”} and the
set B = {x | x is a letter of the words ” TERRIFIC”} are equivalent.

Answer 1

Answer:

a. False

Here, A = {1,2,3} It is the finite subset of infinite set N of natural numbers.

b. False

The set of all squares is contained in the set of all rectangles.

c. False

A infinite set can have infinitely many subsets.

d. True

e. True

f. False

g. True

h. False