CBSE 12th Standard Maths Subject Relations and Functions HOT Questions 4 Mark Questions With Solution 2021
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CBSE 12th Standard Maths Subject Relations and Functions HOT Questions 4 Mark Questions With Solution 2021
12th Standard CBSE
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Reg.No. :
Maths
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Let X = {1, 2, 3, 4, 5, 6, 7, 8, 9}. Let R1 be a relation in X given by R1 = {(x, y)}: x - y is divisible by 3} and R2 be another relation on X given by R2 = {(x, y): (x, y)} \(\subset\) {1, 4, 7} or {x, y} \(\subset\){2, 5, 8} or {x, y} \(\subset\){3, 6, 9}} show that R1 = R2
(a)
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CBSE 12th Standard Maths Subject Relations and Functions HOT Questions 4 Mark Questions With Solution 2021 Answer Keys
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Note that the characteristic of sets {1, 4, 7}, {2, 5, 8} and {3, 6, 9} is that difference between any two elements of these sets is a multiple of 3.
Therefore, (x, y) \(\in\) R1 \(\Rightarrow\) x – y is a multiple of 3 \(\Rightarrow\) {x, y} \(\subset\) {1, 4, 7} or {x, y} \(\subset\) {2, 5, 8} or {x, y} \(\subset\) {3, 6, 9} \(\Rightarrow\) (x, y) \(\in\) R2.
Hence, R1 \(\subset\) R2.
Similarly, {x, y} \(\in\) R2 Þ {x, y}\(\subset\) {1, 4, 7} or {x, y} \(\subset\) {2, 5, 8} or {x, y} \(\subset\) {3, 6, 9} \(\Rightarrow\) x – y is divisible by 3 \(\Rightarrow\) {x, y} \(\in\) R1.
This shows that R2 \(\subset\) R1.
Hence, R1 = R2
