Given: p is true
prove: p _ q is true
assume p and ~q are both true. ~q _ r, and r _ ~p. therefore, ~p and p cannot be true, so p and ~q cannot be true. therefore, p _ q is true.

what type of proof is illustrated above?

a. proof by contradiction
b. proof by law of detachment
c. proof by theorem

Suppose a least-squares regression line is given by modifyingabove y with caret equals 4.302 x minus 3.293. what is the mean value of the response variable if xequals20?

Sophia wrote an equation to represent the revenue of a movie theater for one day. she let x represent the number of child tickets sold and y represents the nunver of adult tickets sold. if a child ticket cost $4, an adult ticket cost $6, and the total revenue for the daybwas $420, which equation could sophia use to represent the number of chikd and adult tickets that were sold?

Is the underlined participial phrase correctly placed or misplaced? i smelled each and every flower strolling through the garden. a. correctly placed participial phrase b. misplaced participial phrase