Class 11

Math

Co-ordinate Geometry

Sets

Let $A={1,2,{3,4},5}$. Which of the following statements are incorrect and why?

(i) ${3,4}⊂A$

(ii) ${3,4}ϵA$

(iii) ${{3,4}}⊂A$

(iv) $1ϵA$

(iv) $1ϵA$

(v) $1⊂A$

(vi) ${1,2,5}⊂A$

(vii) ${1,2,5}ϵA$

(vii) ${1,2,5}ϵA$

(viii) ${1,2,3}⊂A$

(ix) $ϕ ϵA$

(x) $ϕ⊂A$ (xi) ${ϕ}⊂A$

(x) $ϕ⊂A$ (xi) ${ϕ}⊂A$

(i) The statement ${3,4}⊂A$ is incorrect because $3∈{3,4}$; however, $3∈/A$.

(ii) The statement ${3,4}∈A$ is correct because ${3,4}$ is an element of A.

(iii) The statement ${{3,4}}⊂A$ is correct because ${3,4}∈{{3,4}}$ and ${3,4}∈A$.

(iv) The statement $1∈A$ is correct because 1 is an element of A.

(v) The statement $1⊂A$ is incorrect because an element of a set can never be a subset of itself.

(vi) The statement ${1,2,5}⊂$ A is correct because each element of ${1,2,5}$ is also an element of A.

(vii) The statement ${1,2,5}∈A$ is incorrect because ${1,2,5}$ is not an element of A.

(viii) The statement ${1,2,3}⊂A$ is incorrect because $3∈{1,2,3}$; however, $3∈/A$.

(ix) The statement $ϕ∈A$ is incorrect because $ϕ$ is not an element of A.

(x) The statement $ϕ⊂A$ is correct because $ϕ$ is a subset of every set.

(xi) The statement ${ϕ}⊂A$ is incorrect because $ϕϵ{ϕ}$; however, $ϕ∈/A$.