If p → q is true, then ~ q → ~ p is false. always sometimes never

If p → q is true, then ~ q → ~ p is never false.

Step-by-step explanation:

If p → q is true, then we need to check whether the statement ~ q → ~ p is true or false.

Truth table:

p                 q             ~ p             ~ q           p → q            ~ q → ~ p

T                T                F                F                T                T

T                F                F                T                F                F

F                T                T                F               T                T

F                F                T                T               T                T

From the above table it is clear that p → q is true, then ~ q → ~ p is always true.

If p → q is true, then ~ q → ~ p is never false.

b: |12 – x| ≤ 0.25

step-by-step explanation:      

let x be the possible lengths in inches, of the ribbons jaime cut.

we have been given that jaime is cutting strips of ribbon for a project. he tries to cut each piece to be 12 inches long, but sometimes he cuts it too long or too short by as much as 0.25 inch.  

we can represent this information in an inequality as:

by the definition of absolute value function we will get,

upon combining our inequalities we will get,

therefore, the inequality   describes all the possible lengths (x), in inches, of the ribbons jaime cut.

step-by-step explanation: