In each of the following,determine whether the statement is true or false. If it is true,prove it. If it is false,give a counterexample.
If $x \in A$ and $A \in B,$ then $x \in B$.
If $x \in A$ and $A \in B,$ then $x \in B$.
(N/A) The statement is False.
To disprove the statement,we provide a counterexample.
Let $A = \{1, 2\}$ and $B = \{3, 4, \{1, 2\}\}$.
Here,$1 \in A$ and $A \in B$ (since $\{1, 2\}$ is an element of $B$).
However,$1 \notin B$ because $1$ is not one of the elements $\{3, 4, \{1, 2\}\}$.
Thus,the statement is false.
To disprove the statement,we provide a counterexample.
Let $A = \{1, 2\}$ and $B = \{3, 4, \{1, 2\}\}$.
Here,$1 \in A$ and $A \in B$ (since $\{1, 2\}$ is an element of $B$).
However,$1 \notin B$ because $1$ is not one of the elements $\{3, 4, \{1, 2\}\}$.
Thus,the statement is false.
Explore More
Similar Questions
Coordination compounds have great importance in biological systems. In this context,which of the following statements is incorrect?
The reaction $RCOCl + H_2 \xrightarrow{Pd/BaSO_4} RCHO + HCl$ is known as:
Haemozoin is a
The height to which a cylindrical vessel must be filled with a homogeneous liquid,so that the average force with which the liquid presses the side of the vessel is equal to the force exerted by the liquid on the bottom of the vessel,is equal to:
If $a^{1/x} = b^{1/y} = c^{1/z}$ and $b^2 = ac$,then $x + z = $
Vedclass Products
For Students
Vedclass Test Series
Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.
Start Free TrialFor Teachers
Exam Paper Generator
Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.
Try FreeFor Institutes
Online Exam Module
Live online exams with unlimited students, 360° analytics & white-label branding.
See Demo