For which conditions is p ∨ q false? p is true and q is false.
p is true and q is true.
p is false and q is true.
p is false and q is false.

p is false and q is false.

Step-by-step explanation:

Logic Disjunction

Assume p and q are propositions.

The disjunction of p and q, denoted by p ∨ q, is the proposition called "p or q".

The rule for the 'or' operation is: If any of the propositions are true, then the result is also true.

Thus, the disjunction p ∨ q is false when both p and q are false and is true otherwise.

The correct option is the last one:

p is false and q is false.

let soccer = x and golf = y

part a

1st equation: x + y = 125

2nd equation: x = y +45

part b

replace x in the 1st equation with the 2nd one:

y + 45 + y = 125

simplify:

2y + 45 = 125

subtract 45 from each side:

2y = 80

divide both sides by 2:

y = 80/2

y = 40

she plays golf for 40 minutes.

part c

no because she plays soccer for 45 minutes longer than golf 40 +45 =   85 minutes, not 80 minutes.

assuming you mean addition: addition and subtraction are reverse operations.

step-by-step explanation: