For all sets A, B and C, if A ⊂ B, then A ∪ C ⊂ B ∪ C

Question

Determine whether statement are true or false. Justify your answer.

For all sets A, B and C, if A ⊂ B, then A ∪ C ⊂ B ∪ C

Answer 1

True

According to the question,

There are three sets A, B and C

To check: if A ⊂ B, then A ∪ C ⊂ B ∪ C is true or false

Let x ∈ A ∪ C

⇒ x ∈ A or x ∈ C

⇒ x ∈ B or x ∈ C {∵ A ⊂ B}

⇒ x ∈ B ∪ C

⇒ A ∪ C ⊂ B ∪ C

Hence, the given statement “for all sets A, B and C, if A ⊂ B, then A ∪ C ⊂ B ∪ C” is true