Question

complete the truth - tables below.

1. ~p ∨ ~q
2. p ∧ ~r

use the conditional statement “if it is january, then there is snow.” for questions 17 - 18.

1. identify the hypothesis:
2. identify the conclusion:

write the inverse, converse, and contrapositive of the conditional statement below. determine their truth value. if false, explain or give a counterexample.

1. if two angles form a linear pair, then they are supplementary.

inverse:
truth value:
converse:
truth value:
contrapositive:
truth value:

1. write the conditional and converse of the biconditional below. then, determine its truth value.

“a capital letter is a vowel if and only if it is symmetrical.”
conditional:
converse:
truth value of biconditional? explain

Explanation:

17

In a conditional statement "if p, then q", the hypothesis is p. For "If it is January, then there is snow", the hypothesis is the part after "if".

In a conditional statement "if p, then q", the conclusion is q. For "If it is January, then there is snow", the conclusion is the part after "then".

• Inverse: The inverse of a conditional statement "if p, then q" is "if not p, then not q". For "If two - angles form a linear pair, then they are supplementary", the inverse is "If two angles do not form a linear pair, then they are not supplementary". This is false because two non - linear pair angles can still be supplementary (e.g., two separate angles with measures that add up to 180 degrees).
• Converse: The converse of "if p, then q" is "if q, then p". So the converse is "If two angles are supplementary, then they form a linear pair". This is false as supplementary angles do not have to be adjacent (a linear pair is adjacent supplementary angles).
• Contrapositive: The contrapositive of "if p, then q" is "if not q, then not p". The contrapositive is "If two angles are not supplementary, then they do not form a linear pair", which is true because by definition, a linear pair of angles are supplementary.

Answer:

It is January

18