Determine which of the following statements is a tautology or a contradiction.

(i) ~ q ~ p

(ii) p (p v q)

(iii) (p ù q) (p v q)

Ben is three times as old as samantha, who is two years older than half of michel's age. if michel is 12. how old is ben?

Given the system of equations presented here: 2x + 4y = 14 4x + y = 20 which of the following actions creates an equivalent system such that, when combined with the other equation, one of the variables is eliminated? multiply the second equation by â’4 to get â’16x â’ 4y = â’80 multiply the second equation by â’1 to get â’4x â’ y = â’20 multiply the first equation by 2 to get 4x + 8y = 28 multiply the first equation by â’1 to get â’2x â’ 4y = â’14

Aremote-controlled boat can travel at 4 feet per second in calm water. the boat traveled 48 feet with the current, and then it traveled 16 feet against the current in the same amount of time. how fast is the current?