Conditional Statements Skill 09 Objective HSGCO 91011 Students

Conditional Statements Skill 09

Objective HSG-CO. 9/10/11: Students are responsible for recognizing conditional statements and their parts, and writing converses, inverses, and contrapositives of conditionals.

Definitions A conditional is an if-then statement. The hypothesis is the part following the if. The conclusion is the part following then.

Definitions The truth value of a conditional is either true or false. The negation of a statement p is opposite of the statement, the symbol is ~p read “not p”. A counterexample is an example that shows that a conjecture is incorrect.

Definitions The converse of a statement is the exchange of the hypothesis and the conclusion. The inverse of a statement, negate both the hypothesis and conclusion of the conditional. A contrapositive of a statement, negate both the hypothesis and the conclusion of the converse.

Example Converse: Inverse: Contrapositive:

Example 1; Identify hypothesis & conclusion What are the hypothesis and conclusion of the conditional. If an animal is a robin, then the animal is a bird. Hypothesis: an animal is a robin Conclusion: the animal is a bird If an angle measures 130, then the angle is obtuse. Hypothesis: Conclusion: an angle measures 130 the angle is obtuse

Example 2; write a conditional How can you write the following statement as a conditional. “Vertical angles share a vertex. ” If two angles are vertical, then, they share a vertex. “Dolphins are mammals. ” If an animal is a dolphin, then the animal is a mammal.

Example 3; understand conditionals Is the conditional true or false? If it’s false find a counterexample. “If a woman is from Spain, then she is European. ” True, because Spain is a European country, so people from Spain are European. “If a number is divisible by 3, then it is odd. ” False,

Example 4; converse, inverse, & contrapositive Conditional: If the figure is a square, then the figure is a quadrilateral. Converse: If the figure is a quadrilateral, then it is a square. Inverse: If the figure is not a square, then it is not a quadrilateral. Contrapositive: If the figure is not a quadrilateral, then it is not a square.

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