Question

Which of the following is true?

• A. $\mathrm{a}\in \left\{\left\{\mathrm{a}\right\},\mathrm{b}\right\}$
• B. $\left\{\mathrm{b},\mathrm{c}\right\}\in \left\{\mathrm{a},\left\{\mathrm{b},\mathrm{c}\right\}\right\}$
• C. $\left\{\mathrm{a},\mathrm{b}\right\}\in \left\{\mathrm{a},\left\{\mathrm{b},\mathrm{c}\right\}\right\}$
• D. None of these

Answer 1

The correct option is B

$\left\{\mathrm{b},\mathrm{c}\right\}\in \left\{\mathrm{a},\left\{\mathrm{b},\mathrm{c}\right\}\right\}$

Explanation for the correct option:

The symbol $\in$signifies that an element belongs to a set.

The set $\left\{\mathrm{b},\mathrm{c}\right\}$ is an element of the set $\left\{\mathrm{a},\left\{\mathrm{b},\mathrm{c}\right\}\right\}$.

So, $\left\{\mathrm{b},\mathrm{c}\right\}$ belongs to the set $\left\{\mathrm{a},\left\{\mathrm{b},\mathrm{c}\right\}\right\}$.

Explanation for incorrect options:

Option a) $\mathrm{a}\in \left\{\left\{\mathrm{a}\right\},\mathrm{b}\right\}$

Not $\mathrm{a}$ but $\left\{\mathrm{a}\right\}$ is an element of the set $\left\{\left\{\mathrm{a}\right\},\mathrm{b}\right\}$. The brackets are missing.

So, $\mathrm{a}$ does not belong to the set $\left\{\left\{\mathrm{a}\right\},\mathrm{b}\right\}$.

Option c) $\left\{\mathrm{a},\mathrm{b}\right\}\in \left\{\mathrm{a},\left\{\mathrm{b},\mathrm{c}\right\}\right\}$

The set $\left\{\mathrm{a},\mathrm{b}\right\}$ is not an element of the set $\left\{\mathrm{a},\left\{\mathrm{b},\mathrm{c}\right\}\right\}$. The set $\left\{\mathrm{b},\mathrm{c}\right\}$ is an element of the set $\left\{\mathrm{a},\left\{\mathrm{b},\mathrm{c}\right\}\right\}$.

So, $\left\{\mathrm{a},\mathrm{b}\right\}$does not belong to the set $\left\{\mathrm{a},\left\{\mathrm{b},\mathrm{c}\right\}\right\}$

Hence, option b) $\left\{\mathrm{b},\mathrm{c}\right\}\in \left\{\mathrm{a},\left\{\mathrm{b},\mathrm{c}\right\}\right\}$ is true.