Which set of statements always have the same truth value?

Let p and q be two propositional statements,

The conditional of the two statements is

'If p then q'

written symbolically as

The converse is

'If q then p'

written symbolically as

The Inverse is

'If not p then not q'

written symbolically as

The contrapositive is

'If not q then not p'

written symbolically as

In order to determine which pairs have the same truth value, we draw a truth table as in the diagram.

We can see from the diagram that the conditional and the contrapositive have the same truth value.

The correct option is D.

arithmetic sequence

step-by-step explanation:

given that a sequence has terms as

19, 15, 11,

this is represented on a graph

the pattern indicates that the sequence is an arithmetic sequence with i term

a=19 and common difference d =-4

any general term

thus the sequence is reduced by 4 for each successive term starting from 1 and nth term is

24-5n.

first negative term would start after 5th term

5th term =24-25< 0

from 5th term onwards the sequence would be negative.

a

b

d

step-by-step explanation: