Math, asked by xiong123, 4 days ago

Let A={1,2} and {5,4} write A×B, how many subset will A×B have ? list them ?​

Answers

Answered by pavanadevassy
0

Answer:

A\times B will have 16 subsets.

Step-by-step explanation:

If a set has n elements, then it will have 2^n subsets.

Given the sets,

A=\{1,2\}\\\\B=\{5,4\}

Then the cartesian product is,

A\times B=\{(1,5),(1,4),(2,5),(2,4)\}

So there are 4 elements in the set A\times B and thus it has 2^4=16 subsets. We can list them:

\phi, \{(1,5)\},\{(1,4)\},\{(2,5)\},\{(2,4)\},\{(1,5),(1,4)\},\{(1,5),(2,5)\},\{(1,5),(2,4)\},\\\\\{(2,5),(1,4)\},\{(2,4),(1,4)\},\{(2,5),(2,4)\}, \{(1,5),(1,4),(2,5)\},\{(1,5),(1,4),(2,4)\},\\\\\{(1,4),(2,5),(2,4)\},\{(1,5),(2,5),(2,4)\},\{(1,5),(1,4),(2,5),(2,4)\}

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