Question

Examine whether the following statements arc hue or false :
(1) {1, 2, 3} ⊂ {1, 2, 3}
(2) {a, b} ⊄ {b, c, a}
(3) Ф ∉ { Ф }
(4) {3} ⊂ ({1, 2, {3}, 4}

Answer 1

Answer:

1= true 2=false 3= true 4= true

Answer 2

Answer:

(1). True

(2). False

(3). True

(4). True

Step-by-step explanation:

In the question,

(1) {1, 2, 3} ⊂ {1, 2, 3}

This is True.

As

The set is always the subset of its own.

So,

{1, 2, 3} is a subset of {1, 2, 3}.

(2) {a, b} ⊄ {b, c, a}

This is False.

The set {a, b} is subset because, {a} and {b} both are present in the set.

(3) ∅ ∉ {∅}

This is True.

The empty element, ∅, is not a subset of an already empty set. However, an empty set is always a subset of all the sets.

(4) {3} ⊂ {1, 2, {3}, 4}

This is True.

{3} is an element in the set. So it is a subset.