Let P be the set of all subsets of a given set X- Show that - - P - P - P given by A- B - A - B and - - P - P - P given by A- B - A - B are binary operations on the set P-

Name: NCERT - Grade 12 - Mathematics - Relations and Functions - Q74
Uploaded: 2022-07-04T10:36:42+05:30
Description: Check for Union. ∪ : P × P nbsp; nbsp;→ P ( A, B ) nbsp; nbsp; nbsp;→ A ∪ B .P nbsp; nbsp; P is a the set of all subsets of a given set X. Here ...

Check for Union. ∪ : P × P nbsp; nbsp;→ P ( A, B ) nbsp; nbsp; nbsp;→ A ∪ B .P nbsp; nbsp; P is a the set of all subsets of a given set X. Here ...

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Standard VII

History

Rani Abbakkadevi

Let P be the ...

Question

Let $P$ be the set of all subsets of a given set $X$ . Show that $\cup : P \times P \to P$ given by $(A, B) \to A \cup B$ and $\cap : P \times P \to P$ given by $(A, B) \to A \cap B$ are binary operations on the set $P$ .

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Solution

Check for Union.
$\cup : P \times P \to P$

$(A, B) \to A \cup B . P$

$P$ is a the set of all subsets of a given set $X$ .

Here, $A & B$ are in set $P$ , So, $A$ and $B$ are also subsets of $X$

$∴ A \cup B$ will be a subset of $X$ as union of subsets is also a subset

Hence,
$A \cup B$ will also be in set $P$
So, $\cup$ is a binary operation.

Check for intersection.
$\cap : P \times P \to P$

$(A, B) \to A \cap B$

$P$ is a the set of all subsets of a given set $X$ .

Here, $A & B$ are in set $P$ , So, $A$ and $B$ are also subsets of $X$

$∴ A \cap B$ will be a subset of $X$ as union of subsets is also a subset

Hence,
$A \cap B$ will also be in set $P$
So, $\cap$ is a binary operation.

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Let P be the set of all subsets of a given set X. Show that ∪:P×P→P given by (A,B)→A∪B and ∩:P×P→P given by (A,B)→A∩B are binary operations on the set P.

Let $P$ be the set of all subsets of a given set $X$ . Show that $\cup : P \times P \to P$ given by $(A, B) \to A \cup B$ and $\cap : P \times P \to P$ given by $(A, B) \to A \cap B$ are binary operations on the set $P$ .