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Commutative Law of Binary Operation

On the power ...

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On the power set P of a non empty set A we define an operation △ by X△ Y=(X'∩ Y)∪(X∩ Y') Then which are of the following statements is true about △ A. commutative and associative without an identity B.commutative but not associative with an identity C. associative but not commutative without an identity D.associative and commutative with an identity

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Q. On the power set P of a non-empty set A, we define an operation ∆ by

X ∆ Y = (X \cap Y) \cup (X \cap Y)

Then which are of the following statements is true about ∆
(a) commutative and associative without an identity
(b) commutative but not associative with an identity
(c) associative but not commutative without an identity
(d) associative and commutative with an identity

Q. Let * be a binary operation on R defined by a * b = ab + 1. Then, * is
(a) commutative but not associative
(b) associative but not commutative
(c) neither commutative nor associative
(d) both commutative and associative

Q. On Z an operation * is defined by a * b = a² + b² for all a, b ∈ Z. The operation * on Z is
(a) commutative and associative
(b) associative but not commutative
(c) not associative
(d) not a binary operation

*

be a binary operation defined on

R

a * b = \frac{a + b}{4} \forall a, b \in R,

then the operation

*

S

be a non-empty set and

o

be a binary operation on

S

x o y = x : x, y \in S

. Determine whether o is commutative ans associative.

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Commutative Law of Binary Operation

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