Question

Let "p"' represent "The area of rectangle ABCD is 50 square inches." Let "q" represent "The perimeter of rectangle ABCD is 30 inches." Let "r" represent " The Length of rectangle ABCD is twice the width."

Answer 1

1. It is not the case that the perimeter of rectangle ABCD is 30 in.

2. p ^ ~q
^ represents "and"
~ represents negation

3. q v ~p
v represents "or"

4. q v ~p is true if q is true or ~p is true or both are true.
The perimeter of ABCD is 2(6) + 2(9) = 30, so statement q is true.
Therefore, q v ~p is true.

5. p → r is only false if p is true AND r is false.
The perimeter of ABCD is 2(12.5) + 2(4) = 25+8 = 33
Therefore, p is false, so p→r is true.

Answer 2

thank you