Question

Which of the following is/are true?

1. If $A$ is a subset of the universal set $U$, then its complement $A\text{'}$ is also a subset of $U$.

2. If $U=\left\{1,2,3,\dots ..,10\right\}$ and $A=\left\{1,3,5,7,9\right\}$, then $(A\text{'})\text{'}=A$.

• A. Only I is true
• B. Only II is true
• C. Both I and II are true
• D. None of these

Answer 1

The correct option is C

Both I and II are true

Explanation for the correct option

For statement 1:

Using the Venn diagram, we get

Let coloured part is set $A$

According to the Venn diagram, we get $A\text{'}$

Red coloured part is $A\text{'}$.

$A\text{'}$is also a subset of $U$.

Statement 1 is correct.

For statement 2:

Since, $A=\left\{1,3,5,7,9\right\}$, then $A\text{'}=\left\{2,4,6,8,10\right\}$

Now $(A\text{'})\text{'}=\left\{1,3,5,7,9\right\}$ [$\because A\text{'}$is a subset of $U$]

Therefore, $(A\text{'})\text{'}=A$ is correct.

Statement 2 is correct.

Hence, both statements are correct.
Therefore, the correct option is option (c).