Let A={1,2,3,4,…} and B={0,1,2,3,4}. The number of elements in the relation R=(a,b)∈A×A:2(a−b)2+3(a−b)∈B is _____.
Explanation
amp;A={1,2,3,...,10}amp;B={0,1,2,3,4}amp;R={(a,b)∈A×A:2(a−b)2+3(a−b)∈B}
Now 2(a−b)2+3(a−b)
=(a−b)[2(a−b)+3]
⇒a=b or a−b=−2
when a=b⇒10 order pair
when a−b=−2⇒8 order pair
Total = 18
Explanation
amp;A={1,2,3,...,10}amp;B={0,1,2,3,4}amp;R={(a,b)∈A×A:2(a−b)2+3(a−b)∈B}
Now 2(a−b)2+3(a−b)
=(a−b)[2(a−b)+3]
⇒a=b or a−b=−2
when a=b⇒10 order pair
when a−b=−2⇒8 order pair
Total = 18
