2.1 Conditional Statements

Writing conditionals Using definitions as conditional

statements Writing biconditionals Making truth tables

What We Will Learn

Conditional: logical statement that has a hypothesis and conclusion

If-then form: how a conditional is written Hypothesis: if part of if-then Conclusion: then part of if-then Negation: opposite of original statement

Converse: statement written conclusion and then hypothesis

Inverse: negate both hypothesis and conclusion of a conditional

Contrapositive: negate the converse of a conditional

Equivalent statements: when both statements are true or false

Biconditional: phrase containing “if and only if”

Truth value: whether statement is true or false

Truth table: shows whether conditional is true or false based on hypothesis and conclusion

Needed Vocab

Hyp – all birds, con – have feathers If something is a bird, then it has

feathers. Hyp – you are in Texas, con – you are

in Houston. If you are in Texas, then you are in

Houston.

Identify hypothesis and conclusion and write as a conditional

Statement: All birds have feathers You are in Texas if you are in

Houston.

Ex. 1 Writing Conditionals

Hyp – all 30 angles, con – acute angles If an angle measures 30, then it is

an acute angle. Hyp – 2x + 7 = 1, con – x = -3

If 2x + 7 = 1, then x = -3

Identify hypothesis and conclusion and write as Conditional

Statement: All 30 angles are acute angles 2x + 7 = 1 because x = -3

Your Practice

Negation: The ball is not red The cat is black

Statement: The ball is red The cat is not black

Ex. 2 Writing a Negation

Symbolic Forms

Type Words Symbols

Conditional If p, then q p → q

Converse If q, then p q → p

Inverse If not p, then not q ~p → ~q

Contrapositive If not q, then not p ~q → ~p

Biconditional p if and only if q p ↔ q

Let p be “you are a guitar player” and q be “you are a musician.” Write each statement. Conditional:

If you are a guitar player, then you are a musician.

Converse: If you are a musician, then you are a

guitar player. Inverse:

If you are not a guitar player, then you are not a musician.

Contrapositive: If you are not a musician, then you are

not a guitar player.

Ex. 3 Writing Converse, Inverse,

and Contrapositive

Let p be “two angles are supplementary” and let q be “the measures of the angles sum to 180.”

Write each statement Conditional:

If two angles are supplementary, then the measures of the angles sum to 180.

Converse: If the measures of the angles sum to 180,

then the two angles are supplementary.

Inverse: If the two angles are not supplementary,

then the measures of the angles do not sum to 180.

Contrapositive: If the measures of the angles does not

sum to 180, then the two angles are not supplementary.

Your Practice

Definition:

Write conditional and converse of definition and check truth value. If true or false If conditional and converse are

true, then can write a biconditional

Ex. 5 Writing Biconditionals