Let A-B and C be three sets- If A- B and B- C- is it true that A- C - If not- give an example-

Name: NCERT - Grade 11 - Mathematics - Sets - Q23
Uploaded: 2022-07-04T10:36:42+05:30
Description: Let A={ 1 },B={{ 1 },2,3 } And C={{ 1 },2,3,4,5 } Here, A∈ B, also nbsp;B⊂ C Now 1∈ A but nbsp;1∉ C ∴ A⊄C ...

Let A={ 1 },B={{ 1 },2,3 } And C={{ 1 },2,3,4,5 } Here, A∈ B, also nbsp;B⊂ C Now 1∈ A but nbsp;1∉ C ∴ A⊄C ...

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard IX

Mathematics

Subset

Let A,B and C...

Question

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.

Open in App

Solution

Let $A = {1}, B = {{1}, 2, 3}$
And $C = {{1}, 2, 3, 4, 5}$
Here, $A \in B$ , also $B \subset C$
Now $1 \in A$ but $1 \notin C$
$∴ A \subset̸ C$

Suggest Corrections

Similar questions

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 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

Q. Let

A, B

and

C

be sets such that

ϕ \neq A \cap B \subseteq C

. Then which of the following statements is not true ?

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. If

A, B

are any two sets and

C \subset A ⋃ B

. Then is it true that

C \subseteq A

C \subseteq B

Join BYJU'S Learning Program

Explore more

Subset

Standard IX Mathematics

Join BYJU'S Learning Program

Let A,B and C be three sets. If A∈B and B⊂C, is it true that A⊂C ?. If not, give an example.

Let A={1},B={{1},2,3} And C={{1},2,3,4,5} Here, A∈B, also B⊂C Now 1∈A but 1∉C ∴A⊄C

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 $A = {1}, B = {{1}, 2, 3}$
And $C = {{1}, 2, 3, 4, 5}$
Here, $A \in B$ , also $B \subset C$
Now $1 \in A$ but $1 \notin C$
$∴ A \subset̸ C$