Question

Which of the following is a true statement

(a) {a} ∈ {a, b, c} (b) {a} ⊆ {a, b, c}

(c) φ ∈ {a, b, c} (d) None of these
please give this answer with proof​

Answer 1

Answer:

(b) because {a} is a subset of given set{a,b,c}

Answer 2

Concept:

If every component of Set A is also present in Set B, then Set A is said to be a subset of Set B. To put it another way, Set B contains Set A.

As an illustration, if set A has the elements X, Y, and set B contains the elements X, Y, and Z, then set A is the subset of set B.

A subset is represented in set theory by the symbol ⊆, which means "is a subset of."

When there are "n" elements in a set, there are 2ⁿ subsets of that set, and there are 2ⁿ-1 proper subsets of that subset.

Given:

(a) {a} ∈ {a, b, c} (b) {a} ⊆ {a, b, c}

(c) φ ∈ {a, b, c} (d) None of these

Find:

Which of the following is a true statement

Solution:

(a) {a} ∈ {a, b, c}

a belongs to {a,b,c} not {a}

So, option a is wrong

(b) {a} ⊆ {a, b, c}

{a} is the subset of {a, b, c}

So,option b is correct

(c) φ ∈ {a, b, c}

  φ is the subset of  {a, b, c}, but doesnot belong to {a, b, c}

So, option C is wrong

Therefore, option B is corret

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