Suppose a+b=c+d, and `alt c`. Use proof by contradiction to show `b gt d`.

Let r be a rational number and x be an irrational number. Use proof by contradiction to show that r+x is an irrational number.

If a+i b=c+i d , then

Use proof by contradiction to show that there is no value of n for which 6n ends with the digit zero.

Use proof by contradiction to prove that if for an integer a, a^2 is even, then so is a.

Use proof by contradiction to prove that if for an integer a, a^2 is divisible by 3, then a is divisible by 3.

If a +b+c = alphad, b+c+d=beta a and a, b, c are non-coplanar, then the sum of a +b+c+d =

Suppose a, b, c, in R and abc = 1, if A = [[3a, b, c ],[b, 3c, a ],[c, a, 3b]] is such that A ^(T) A = 4 ^(1//3) I and abs(A) gt 0, the value of a^(3) + b^(3) + c^(3) is

Identify A, B, C and D in the following reactions: