> #mathematics , #relations > 5, Let $$R$$ is arelation on the ret $$A=\{1,2,3,4$$ $$5,6\}$$ detined b4 $$R=4(a,+b) ; a+b <=9$$. i) Lest the element of $$R$$ ii) is $$R=R^{-1}$$.?
Mar 14

# 5, Let $$R$$ is arelation on the ret $$A=\{1,2,3,4$$ $$5,6\}$$ detined b4 $$R=4(a,+b) ; a+b <=9$$. i) Lest the element of $$R$$ ii) is $$R=R^{-1}$$.?

5, Let $$R$$ is arelation on the ret $$A=\{1,2,3,4$$ $$5,6\}$$ detined b4 $$R=4(a,+b) ; a+b <=9$$.
i) Lest the element of $$R$$
ii) is $$R=R^{-1}$$.
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Mar 14
i) The elements of $$R$$ can be found by plugging in all possible pairs of elements from set $$A$$ into the relation $$R=4(a+b)$$ where $$a+b \leq 9$$.

So, the elements of $$R$$ are:
$$R = \{4(1+1), 4(1+2), 4(1+3), 4(1+4), 4(1+5), 4(1+6), 4(2+2), 4(2+3), 4(2+4), 4(2+5), 4(2+6), 4(3+3), 4(3+4), 4(3+5), 4(3+6), 4(4+4), 4(4+5), 4(4+6), 4(5+5), 4(5+6), 4(6+6)\} \( R = \{8, 12, 16, 20, 24, 28, 16, 20, 24, 28, 32, 24, 28, 32, 36, 32, 36, 40, 40, 44, 48\}$$

ii) To check if $$R = R^{-1}$$, we need to find the inverse of $$R$$. The inverse of a relation $$R$$ is the set of all pairs $$(b, a)$$ such that $$(a, b)$$ is in $$R$$.

So, the inverse of $$R$$ is:
$$R^{-1} = \{(8, 1), (12, 1), (16, 1), (20, 1), (24, 1), (28, 1), (16, 2), (20, 2), (24, 2), (28, 2), (32, 2), (24, 3), (28, 3), (32, 3), (36, 3), (32, 4), (36, 4), (40, 4), (40, 5), (44, 5), (48, 6)\}$$

Since $$R$$ and $$R^{-1}$$ are not equal, $$R \neq R^{-1}$$.
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