Use De Morgan's law for quantified statements and the laws of propositional logic to show the following equivalences:
(a) Vr (P(2) A-Q(x)) = 3r (-P(2) VQ(x))
(b) Vr (-P(z) → Q(2)) = 3r (-P(2)A-Q())
(c) -3x (-P(x) V (Q(2)^-R(z))) = Vz(P(2)^(-Q(x) V R()))

option 1 is correct.

step-by-step explanation:

y varies inversely with x and constant of variation is 4

the equation will be:

y = k/x

where k =4 so,

y = 4/x

if we put values of x of option 1 in the above equation and find values of y

y = 4/-2 => y =-2

y = 4/-1 => y = -4

y = 4/1 => y = 4

y = 4/2 => y =2

so, all the values of x and y are correct.

if we put values of x given in other options and find value of y we cannot find whole table satisfying the equation.

hence option 1 is correct.

c

step-by-step explanation:

answer: 48

just remember to use pemdas:

parentheses

expressions

multiplication

division

addition

subtraction

is there a picture

step-by-step explanation: