Hallition
properly
8. if 4x = 40, then x = 10.

a. 1/(2^n)

b. ¾

Step-by-step explanation:

a. Given that there are n variables in a compound proposition.

Each of the n variables have exactly two possible equally likely truth values that can be assigned.

The values are true or false.

And the value can only be either true or false at any given time

True(1) + False (1) = 2 truth values

So, the probability of each possible assignment of truth values to the n variables is 1/(2^n)

b. Given that a clause is in disjunctive form of exactly two distinct variables

n = 2 distinct variables; n = 2

1/(2^n) becomes

1/2²

= ¼

This means that there's exactly 1 combination out of possible 2² that will lead to the clause being false.

The probability that a given clause is true, given the random assignment of truth values from part (a) is calculated as 1 - ¼

= ¾