If $A$ and $B$ are two equal sets, then which of the following is not true?

A \subseteq B

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B \subseteq A

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A \in B

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B \notin A

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Solution

The correct option is C $A \in B$
$A \subseteq B$ is true because equal sets are subsets of each other.

$B \subseteq A$ is also true because equal sets are subsets of each other.

Let set $A = {a, b, c}$ and set $B = {a, b, c}$ [ $A$ and $B$ are equal sets]
$a \in B, b \in B, c \in B$
But ${a, b, c} \notin B$
$⟹ A \notin B$
It means $A$ is a subset of $B$ , but $A$ is not an element of $B$ .
So, $A \in B$ is not true.

Let set $A = {a, b, c}$ and set $B = {a, b, c}$ [ $A$ and $B$ are equal sets]
$a \in A, b \in A, c \in A$
But ${a, b, c} \notin A$
$⟹ B \notin A$ which is true.

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