Question - Vedclass

English

Gujarati

Hindi

1.Set Theory

easy

In each of the following, determine whether the statement is true or false. If it is true, prove it. If it is false, give an example.

If $x \in A$ and $A \in B,$ then $x \in B$

Solution

False

Let $A=\{1,2\}$ and $B=\{1,\{1,2\},\{3\}\}$

Now, $2 \in\{1,2\}$ and $\{1,2\}$ $\in\{\{3\}, 1,\{1,2\}\}$

$\therefore A \in B$

Howerer, $2 \notin\{\{3\}, 1,\{1,2\}\}$

Std 11

Mathematics

Share

Similar Questions

Which of the following sets are finite or infinite.

The set of positive integers greater than $100$

easy

Let $A, B,$ and $C$ be the sets such that $A \cup B=A \cup C$ and $A \cap B=A \cap C$. Show that $B = C$

medium

From the sets given below, select equal sets:

$A=\{2,4,8,12\}, B=\{1,2,3,4\}, C=\{4,8,12,14\}, D=\{3,1,4,2\}$

$E=\{-1,1\}, F=\{0, a\}, G=\{1,-1\}, H=\{0,1\}$

medium

Examine whether the following statements are true or false :

$\{a\} \subset\{a, b, c\}$

easy

Write the following sets in the set-builder form :

$\{ 3,6,9,12\}$

easy