Determine whether each argument is valid. If the argument is valid, give a proof using the laws of logic. If the argument is invalid, give values for the predicates P and Q over the domain {a, b} that demonstrate the argument is invalid. (a) ∃x (P(x) ∧ Q(x)) ∴ ∃x Q(x) ∧ ∃x P(x)
(b) ∀x (P(x) ∨ Q(x)) ∴ ∀x Q(x) ∨ ∀x P(x)

7x+8y=-18, 4x-9y=-3 solve the system of equations

The frequency table shows the results of a survey comparing the number of beach towels sold for full price and at a discount during each of the three summer months. the store owner converts the frequency table to a conditional relative frequency table by row. which value should he use for x? round to the nearest hundredth. 0.89 0.90 0.92 0.96

Aword processing program requires a 7- digit registration code made up of the digits 1,2,4,5,6,7 and 9 each number has to be used and no number can be used mor than once how many codes are possible