Let R be a relation from N to N defined by R - a - b - a - b - N- and -a - b 2- Are the following true-i a - a - R for all a - Nii a - a - R implies b - a - Riii a - b - R - b - c - R implies a - c - RJustify your answer in each case-

Here, R = (a, b): a, b ϵ N and a = b^2. (i) No, (3, 3) ϵ̸ R because 3 ≠ 3^2 (ii) No, (9, 3) ϵ R but (3, 9) ϵ̸ R (iii) No, (81, 9) ϵ R, (9, 3) ϵ R but (81, 3 ...

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Standard XI

Mathematics

Intersection

Let R be a re...

Question

Let R be a relation from N to N defined by $R = {(a, b) : a, b ϵ N$ and $a = b^{2}$ }. Are the following true?

(i) $(a, a) ϵ R$ for all $a ϵ N$

(ii) $(a, a) ϵ R$ implies $(b, a) ϵ R$

(iii) $(a, b) ϵ R, (b, c) ϵ R$ implies $(a, c) ϵ R$

Justify your answer in each case.

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Solution

Here, R = {(a, b): a, b $ϵ N$ and $a = b^{2}$ }.

(i) No, $(3, 3) / ϵ R$ because $3 \neq 3^{2}$

(ii) No, $(9, 3) ϵ R$ but $(3, 9) / ϵ R$

(iii) No, $(81, 9) ϵ R, (9, 3) ϵ R$ but $(81, 3) / ϵ R .$

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Let R be a relation from N to N defined by R = {(a, b): a, b ∈ N and a = b²}. Are the following true?

(i) (a, a) ∈ R, for all a ∈ N

(ii) (a, b) ∈ R, implies (b, a) ∈ R

(iii) (a, b) ∈ R, (b, c) ∈ R implies (a, c) ∈ R.

Justify your answer in each case.

Q. Let R be a relation from N to N defined by R = {( a , b ): a , b ∈ N and a = b 2 }. Are the following true? (i) ( a , a ) ∈ R, for all a ∈ N (ii) ( a , b ) ∈ R, implies ( b , a ) ∈ R (iii) ( a , b ) ∈ R, ( b , c ) ∈ R implies ( a , c ) ∈ R. Justify your answer in each case.

Let R be a relation from N to N defined by R = {(a, b): a, b $\in$ N and a = $b^{2}$ }. Which of the following is/are true?

(i) (a, a) $\in$ R, for all a $\in$ N

(ii) (a, b) $\in$ R, implies (b, a) $\in$ R

(iii) (a, b) $\in$ R, (b, c) $\in$ R implies (a, c) $\in$ R

Q. Let R be a relation from N to N defined by R = [(a, b) : a, b ∈ N and a = b²].
Are the following statements true?

(i) (a, a) ∈ R for all a ∈ N
(ii) (a, b) ∈ R ⇒ (b, a) ∈ R
(iii) (a, b) ∈ R and (b, c) ∈ R ⇒ (a, c) ∈ R

Let R be a relation from N to N defined by R = {(a, b) : $a, b ϵ N$ and $a = b^{2}$ }.

Are the following statements true ?

(i) $(a, a) ϵ R$ for all $a ϵ N$

(ii) $(a, b) ϵ R \Rightarrow (b, a) ϵ R .$

(iii) $(a, b) ϵ R$ and $(b, c) ϵ R \Rightarrow (a, c) ϵ R .$

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Let R be a relation from N to N defined by R={(a,b):a,b ϵ N and a=b2}. Are the following true? (i) (a,a) ϵ R for all a ϵ N (ii) (a,a) ϵ R implies (b,a) ϵ R (iii) (a,b) ϵ R,(b,c) ϵ R implies (a,c) ϵ R Justify your answer in each case.

Here, R = {(a, b): a, b ϵ N and a=b2}. (i) No, (3,3)/ϵ R because 3≠32 (ii) No, (9,3) ϵ R but (3,9)/ϵ R (iii) No, (81,9) ϵ R,(9,3) ϵ R but (81,3)/ϵ R.

Let R be a relation from N to N defined by $R = {(a, b) : a, b ϵ N$ and $a = b^{2}$ }. Are the following true?

(i) $(a, a) ϵ R$ for all $a ϵ N$

(ii) $(a, a) ϵ R$ implies $(b, a) ϵ R$

(iii) $(a, b) ϵ R, (b, c) ϵ R$ implies $(a, c) ϵ R$

Justify your answer in each case.

Here, R = {(a, b): a, b $ϵ N$ and $a = b^{2}$ }.

(i) No, $(3, 3) / ϵ R$ because $3 \neq 3^{2}$

(ii) No, $(9, 3) ϵ R$ but $(3, 9) / ϵ R$

(iii) No, $(81, 9) ϵ R, (9, 3) ϵ R$ but $(81, 3) / ϵ R .$