Let x be non-empty set- P x be its power set- Let - be an operation defined on element of P x b y - A - B - A - B - A - B - P x - Theni Prove that - is a binary operation in P x ii is - associative-iii Is - commutative-

P(x)=A*B #160;Since the operands are only 2 it is a binary operator. A∩ (B∩ C)=(A∩ B)∩ C Associative. A∩ B=B∩ A Commutative. ...

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Standard XII

Mathematics

Binary Operation

Let x be no...

Question

Let $x$ be non-empty set. $P (x)$ be its power set. Let * be an operation defined on element of $P (x) b y, A * B =$
$A \cap B \forall A, B \in P (x) .$ Then
(i) Prove that * is a binary operation in $P (x)$
(ii) is * associative?
(iii) Is * commutative?

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Solution

$P (x) = A * B$
Since the operands are only $2$ it is a binary operator.
$A \cap (B \cap C) = (A \cap B) \cap C ⟹$ Associative.
$A \cap B = B \cap A ⟹$ Commutative.

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Let x be non-empty set. P(x) be its power set. Let * be an operation defined on element of P(x)by,A∗B= A∩B∀A,B∈P(x). Then(i) Prove that * is a binary operation in P(x)(ii) is * associative?(iii) Is * commutative?

P(x)=A∗B Since the operands are only 2 it is a binary operator.A∩(B∩C)=(A∩B)∩C⟹ Associative.A∩B=B∩A⟹ Commutative.

Let $x$ be non-empty set. $P (x)$ be its power set. Let * be an operation defined on element of $P (x) b y, A * B =$
$A \cap B \forall A, B \in P (x) .$ Then
(i) Prove that * is a binary operation in $P (x)$
(ii) is * associative?
(iii) Is * commutative?

$P (x) = A * B$
Since the operands are only $2$ it is a binary operator.
$A \cap (B \cap C) = (A \cap B) \cap C ⟹$ Associative.
$A \cap B = B \cap A ⟹$ Commutative.