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CBSE Class 11-science Answered

A×(B∩C)=(A×B)∩(A×C) prove tht  
Asked by saiaparnalove5888 | 28 Sep, 2020, 11:27: AM
Expert Answer
To prove: A×(B∩C)=(A×B)∩(A×C)
Let space left parenthesis straight x comma space straight y right parenthesis element of straight A cross times open parentheses straight B intersection straight C close parentheses
rightwards double arrow straight x element of straight A comma space straight y element of straight B intersection straight C
rightwards double arrow straight x element of straight A comma space straight y element of straight B space and space straight y element of straight C
rightwards double arrow open parentheses straight x comma space straight y close parentheses element of straight A cross times straight B space and space open parentheses straight x comma space straight y close parentheses element of straight A cross times straight C
rightwards double arrow open parentheses straight x comma space straight y close parentheses element of open parentheses straight A cross times straight B close parentheses intersection open parentheses straight A cross times straight C close parentheses
Now comma space suppose space open parentheses straight x comma space straight y close parentheses element of open parentheses straight A cross times straight B close parentheses intersection open parentheses straight A cross times straight C close parentheses
rightwards double arrow open parentheses straight x comma space straight y close parentheses element of straight A cross times straight B space and space open parentheses straight x comma space straight y close parentheses element of straight A cross times straight C
rightwards double arrow straight x element of straight A space and space straight y element of straight B space & space straight x element of straight A space and space straight y element of straight C
rightwards double arrow straight x element of straight A comma space straight y element of straight B space and space straight y element of straight C
rightwards double arrow straight x element of straight A comma space straight y element of straight B intersection straight C
rightwards double arrow left parenthesis straight x comma space straight y right parenthesis element of straight A cross times open parentheses straight B intersection straight C close parentheses
Thus comma space left parenthesis straight x comma space straight y right parenthesis element of straight A cross times open parentheses straight B intersection straight C close parentheses left right double arrow open parentheses straight x comma space straight y close parentheses element of open parentheses straight A cross times straight B close parentheses intersection open parentheses straight A cross times straight C close parentheses
Hence comma space straight A cross times open parentheses straight B intersection straight C close parentheses equals open parentheses straight A cross times straight B close parentheses intersection open parentheses straight A cross times straight C close parentheses
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