Question

If $A\subset b$ and $B \in C$, then A \in C[/tex]. State whether the statement is True (or) False And Justify it

Answer 1

Answer:

The given statement is true

Step-by-step explanation:

$\text{Given : }$

$A\subseteq\,B\:\text{ and }B\subseteq\,C$

$\text{Let }x\in\,A$

$\text{since A is a subset of B, each element of A is also an element of B}$

$\implies\,x\in\,B$

$\text{since B is a subset of C, each element of B is also an element of C}$

$\implies\,x\in\,C$

$\text{But }x\in\,A\text{ is arbitrary}$

$\text{Hence each element of A is also an element of B}$

$\therefore\,A\subseteq\,C$

Answer 2

$\displaystyle\huge\red{\underline{\underline{Solution}}}$

DEFINITION

SUBSET : A set A is said to be a subset of B if every element of A is an element of B but not the converse

$\sf{In \: set \: form \: it \: is \: written \: as \: \: A \subset \: B}$

GIVEN

$\sf{ \: A \subset \: B \: \: \: and \: \: \: \: B \subset \: C \: }$

TO JUSTIFY

$\sf{ \: A \subset \: C \: }$

CALCULATION

YES THE STATEMENT IS TRUE

JUSTIFICATION

$\sf{Let \: \: x \in \: A \: }$

$\sf{ \implies \: \: x \in \: B} \: \: \: ( \because \: A \subset B \: )$

$\sf{ \implies \: \: x \in \: C} \: \: \: ( \because \: B \subset C \: )$

$\sf{Hence \: x \in A \: \: implies \: \: \: x \in C }$

$\sf{So \: \: \: A \subset C}$

Hence the justification follows

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LEARN MORE FROM BRAINLY

if A ={2,3} and B= { x|x is solution of x^2 + 5x + 6= 0}

Are there A and B equal set or disjoint set?

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