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Ordered Pair

Let A=a,e,i,o...

Question

Let A={a,e,i,o,u} and B={a,b,c,d}. Is A a subset of B? No. (Why?) Is B a subset of A? No. (Why?)

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Solution

$A = {a, e, i, o, u}$ and $B = {a, b, c, d}$

$(i)$ For a set to be a subset of another set, it needs to have all elements present in the another set.
In set $A, {e, i, o, u}$ elements are present but these are not present in set $B$
Hence $A$ is not a subset of $B$ .

$(i i)$ For this condition to be true, are elements of sets $B$ should be present in set $A$
In set $B, {b, c, d}$ elements are present but these elements are not present in set $A$
Hence $B$ is not a subset of $A$

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

(i) {3, 4} $\subset$ A (ii) {3, 4} $\in$ A

(iii) {{3, 4}} $\subset$ A (iv) $1 \in A$

(v) $1 \subset A$ (vi) {1, 2, 5} $\subset$ A

(vii) {1, 2, 5} $\in$ A (viii) {1, 2, 3} $\subset$ A

(ix) $Φ \in A$ (x) $Φ \subset A$

(xi) { $Φ$ } $\subset$ A.

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

(i) {3, 4}⊂ A

(ii) {3, 4}}∈ A

(iii) {{3, 4}}⊂ A

(iv) 1∈ A

(v) 1⊂ A

(vi) {1, 2, 5} ⊂ A

(vii) {1, 2, 5} ∈ A

(viii) {1, 2, 3} ⊂ A

(ix) Φ ∈ A

(x) Φ ⊂ A

(xi) {Φ} ⊂ A

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