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CBSE Class 12-science Answered

If A={a:a∈N,1≤a≤6} and B={b:b∈Z and −2≤b≤4} , find number of elements common on A×B and B×A is

Asked by Ajayram2005 | 26 Sep, 2020, 08:33: AM
Expert Answer
This can be solved as follows:
straight A equals open curly brackets straight a colon straight a element of straight N comma space 1 less or equal than straight a less or equal than 6 close curly brackets space and space straight B equals open curly brackets straight b colon straight b element of straight Z comma space minus 2 less or equal than straight b less or equal than 4 close curly brackets
1 less or equal than straight a less or equal than 6 space rightwards double arrow space straight a equals 1 comma space 2 comma space 3 comma space 4 comma space 5 comma space 6
minus 2 less or equal than straight b less or equal than 4 space rightwards double arrow space straight b equals negative 2 comma negative 1 comma space 0 comma space 1 comma space 2 comma space 3 comma space 4
rightwards double arrow straight A equals open curly brackets 1 comma space 2 comma space 3 comma space 4 comma space 5 comma space 6 close curly brackets space and space straight B equals open curly brackets negative 2 comma space minus 1 comma space 0 comma space 1 comma space 2 comma space 3 comma space 4 close curly brackets
straight A cross times straight B equals open curly brackets open parentheses 1 comma space minus 2 close parentheses comma space left parenthesis 1 comma negative 1 right parenthesis comma space left parenthesis 1 comma space 0 right parenthesis comma space left parenthesis 1 comma space 1 right parenthesis comma space left parenthesis 1 comma space 2 right parenthesis comma space left parenthesis 1 comma space 3 right parenthesis comma space left parenthesis 1 comma space 4 right parenthesis... close curly brackets
straight B cross times straight A equals open curly brackets open parentheses negative 2 comma space 1 close parentheses comma space open parentheses negative 2 comma space 2 close parentheses comma space open parentheses negative 2 comma space 3 close parentheses comma space open parentheses negative 2 comma space 4 close parentheses comma space open parentheses negative 2 comma space 5 close parentheses comma space open parentheses negative 2 comma space 6 close parentheses... close curly brackets
straight A cross times straight B space intersection space straight B cross times straight A space equals space open curly brackets open parentheses 1 comma space 1 comma space left parenthesis 1 comma space 2 right parenthesis comma space left parenthesis 1 comma space 3 right parenthesis comma space left parenthesis 1 comma space 4 right parenthesis comma space left parenthesis 2 comma space 1 right parenthesis comma space... space left parenthesis 2 comma space 4 right parenthesis comma space left parenthesis 3 comma space 1 right parenthesis comma space... space left parenthesis 3 comma space 4 close parentheses comma space left parenthesis 4 comma space 1 right parenthesis comma space... space left parenthesis 4 comma 4 right parenthesis close curly brackets
Answered by Renu Varma | 27 Sep, 2020, 01:24: PM
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