Sets — Important Questions

ϕ

The empty set (null set/void set) is denoted by ϕ or {}. {0} is a singleton containing zero. {ϕ} is a set containing the empty set — it has one element.

Set of all prime numbers less than 100

A finite set has a definite number of elements. Prime numbers less than 100 is a bounded, countable set (there are 25 primes less than 100). The others are infinite sets.

8

In sets, elements are listed without repetition. Letters in MATHEMATICS: M, A, T, H, E, M, A, T, I, C, S → distinct letters: M, A, T, H, E, I, C, S → 8 distinct letters.

A = B because they have the same elements

In sets, order of elements does not matter. {a, b, c} and {c, b, a} contain exactly the same elements, so A = B.