If 150 degrees is an acute angle then its supplement is an abuse angle?what is the converse,inverse and contrapositive of this statement?
statement: p => q
converse: q => p
contrapositive: -q => ~p
inverse: ~p => ~q
To determine the converse, inverse, and contrapositive of a statement, it is helpful to first understand the original statement:
Original statement: "If 150 degrees is an acute angle, then its supplement is an obtuse angle."
Converse: In the converse, you switch the hypothesis and conclusion of the original statement. So the converse is: "If the supplement of an angle is an obtuse angle, then the angle is acute."
To explain how to get the answer to the converse: Start by identifying the hypothesis and conclusion of the original statement. The hypothesis is "150 degrees is an acute angle," and the conclusion is "the supplement is an obtuse angle." Then, switch the positions of the hypothesis and conclusion in the converse statement.
Inverse: In the inverse, you negate both the hypothesis and conclusion of the original statement. So the inverse is: "If 150 degrees is not an acute angle, then its supplement is not an obtuse angle."
To explain how to get the answer to the inverse: Begin by identifying the hypothesis and conclusion in the original statement. Negate each part by adding "not" or "is not" to the statement.
Contrapositive: In the contrapositive, you both switch the hypothesis and conclusion and negate them. So the contrapositive is: "If the supplement of an angle is not an obtuse angle, then the angle is not acute."
To explain how to get the answer to the contrapositive: Start by identifying the hypothesis and conclusion in the original statement. Switch their positions and negate each part by adding "not" or "is not" to the statement.
Remember, the converse, inverse, and contrapositive of a statement may or may not be true. They are simply different ways to rephrase the original statement.