Let ω be a set of variables. we say that a propositional formula is a literal if the formula is equal to x or ¬x for x ∈ ω. we say that a propositional formula on ω is in conjunctive normal form if it is equal to =1 =1 ψi, j , where ψi, j is a literal. let φ be a propositional formula on ω. show using structural induction that there is a propositional formula ψ on ω in conjunctive normal form such that ψ |rho = φ |rho for any assignment rho to ω.

36

step-by-step explanation:

( - 4 , -7 )

all the lines must parallel  

step-by-step explanation:

coordinates of c = ( - 1 , 2 )

3 units left = ( -4 , 2 )

9 units down = ( - 4 , 11 )

a and c

for infinitely many solutions we require both left and right sides to be equal

distribute and simplify

a

14 - 8x = 20 - 8x - 6 = 14 - 8x ← both sides equal so infinite solutions

b

6x - 54 = 6x - 54 + x = 7x - 54 ← not equal

c

4x + 16 = 4x + 10 + 6 = 4x + 16 ← both sides equal so infinite solutions

d

5x - 40 + 10 = 5x + 10

5x - 30 = 5x + 10 ← not equal