Question

2. Prove the statement is true, or find a counter example to show it is false. vx,y ER,√x+y = √x + √y bru 3. True or False? All occurrences of the letter t in the phrase Good Luck are lowercase. Justify your answer. (4) (4) 2

Answer 1

For the first statement, we need to prove that for all real numbers x and y, √x+y = √x + √y is true.

To prove this statement is true, we can square both sides of the equation: (√x + √y)^2 = x + y + 2√xy x + y + 2√xy = x + y + 2√xy Therefore, the statement is true for all real numbers x and y.

For the second statement, we need to determine if all occurrences of the letter t in the phrase "Good Luck" are lowercase.

This statement is false. There is one occurrence of the letter t that is uppercase in the phrase "Good Luck", which is the "T" in "Good". Therefore, the statement is false.

Step-by-step explanation: