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Standard VIII

Mathematics

Union of Sets

let A , B and...

Question

let A , B and C be three sets. if A belongs to B and B is a subset of C , is it true that A is a subset of C? if not , give an example

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Solution

Yes, it is true A is also subset C.

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Similar questions

Q. Let

A, B

and

C

be three sets. If

A \in B

and

B \subset C

, is it true that

A \subset C

?. If not, give an example.

Let A, B ,C be three sets . If A is subset of B abd B belnngs to c, is it true that A belongs to C ? If not given qn example

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

(i)

x \in A

and

A \in B

, then

x \in B

(i i)

A \subset B

and

B \in C

, then

A \in C

(i i i)

A \subset B

and

B \subset C

, then

A \subset C

(i v)

A \subset̸ B

and

B \subset̸ C

, then

A \subset̸ C

(v)

x \in A

and

A \subset̸ B

, then

x \in B

(v i)

A \subset B

and

x \notin B

, then

x \notin A

Q. 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.
(i) If

x \in A

and

A \in B

, then

x \in B

(ii) If

A \subset B

and

B \in C

, then

A \in C

(iii) If

A \subset B

and

B \subset C

, then

A C

(iv) If

A \subset̸ B

and

B \subset̸ C

, then

A \subset̸ C

(v) If

x \in A

and

A \subset̸ B

, then

x \in B

(vi) If

A \subset B

and

x \notin B

, then

x \notin A

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.

(i) If $x \in A$ and $A \in B$ then $x \in B$

(ii) If $A \subset B$ and $B \in C$ then $A \in C$

(iii) If $A \subset B$ and $B \subset C$ then $A \subset C$

(iv) If $A \subset̸ B$ and $B \subset̸ C$ then $A \subset̸ C$

(v) If $x \in A$ and $A \subset̸ B$ then $x \in B$

(vi) If $A \subset B$ and $x \notin B$ then $x \notin A .$

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