Solution - Examine Whether the Following Statements Are True Or False: Subset {A, B} ⊄ {B, C, A} - Subsets

Show that the following four conditions are equivalent:

(i) A ⊂ B

(ii) A – B = Φ

(iii) A ∪ B = B 

(iv) A ∩ B = A

Examine whether the following statements are true or false:

{a} ∈ (a, b, c)

Examine whether the following statements are true or false:

{x: x is an even natural number less than 6} ⊂ {x: x is a natural number which divides 36}

Determine whether the statement is true or false. If it is true, prove it. If it is false, give an example.

If A ⊂ B and x ∉ B, then x ∉ A

Write down all the subsets of the following sets:

(i) {a}

(ii) {a, b}

(iii) {1, 2, 3}

(iv) Φ