Let S be the set of all ordered pairs (x, y) of positive integers sat

1.	Let S be the set of all ordered pairs (x, y) of positive integers satisfying the condition x2 - y2 = 12345678. Then,(a) S is an infinite set(b) S is the empty set(c) S has exactly one element(d) S is a finite set and has at least two elements.
Answer» Answer is : (b) S is the empty set x and y are positive integer x² - y² = 12345678 RHS 12345678 is and even number and last digit is 8. ∴ The last digit of x be 3, 7 and the last digit of y be 1, 9 ∴x and y must be odd and square of difference is multiple of 8 but RHS is not multiple of 8. ∴ S is the empty set.

Let S be the set of all ordered pairs (x, y) of positive integers satisfying the condition x2 - y2 = 12345678. Then,(a) S is an infinite set(b) S is the empty set(c) S has exactly one element(d) S is a finite set and has at least two elements.

Answer»

Answer is : (b) S is the empty set

x and y are positive integer

x² - y² = 12345678

RHS 12345678 is and even number and last digit is 8.

∴ The last digit of x be 3, 7

and the last digit of y be 1, 9

∴x and y must be odd and square of difference is multiple of 8 but RHS is not multiple of 8.

∴ S is the empty set.

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Let S be the set of all ordered pairs (x, y) of positive integers satisfying the condition x2 - y2 = 12345678. Then,(a) S is an infinite set(b) S is the empty set(c) S has exactly one element(d) S is a finite set and has at least two elements.

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