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Consider a binary operation * on N defin...

Consider a binary operation `*` on N defined as `a" "*" "b" "=a^3+b^3` . Choose the correct answer. (A) Is `*` both associative and commutative? (B) Is `*` commutative but not associative? (C) Is `*` associative but not commutative? (D) Is

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In N, `a * b = a^(3) + b^(3)`
Let `a, b in N`
`a* b = a^(3) +b^(3)`
`= b^(3) + a^(3) = b * a`
`therefore ` Operation * is commutative.
Again, let a, b,c `in`N.
`therefore a* (b *c) = a(b^(3) + c^(3))`
`" "=a^(3) + (b^(3) + c^(3))^(3)`
`and (a*b) *c = (a^(3) + b^(3)) *c `
` " "= (a^(3) + b^(3))^(3) + c^(3)`
`therefore" " a* (b*c) ne (a*b)*c`
`rArr` Operation * is not associative.
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