Question

example 3 use the law of syllogism to draw a valid conclusion from each set of given statements, if possible. if no valid conclusion can be drawn, write no valid conclusion and explain your reasoning. 12. if you interview for a job, then you wear a suit. if you interview for a job, then you will update your resume. 13. if tina has a grade point average of 3.0 or greater, she will be on the honor roll. if tina is on the honor roll, then she will have her name in the school paper. 14. if two lines are perpendicular, then they intersect to form right angles. lines s and r form right angles. 15. if the measure of an angle is between 90° and 180°, then it is obtuse. if an angle is obtuse, then it is not acute. 16. if two lines in a plane are not parallel, then they intersect. if two lines intersect, then they intersect in a point. 17. if a number ends in 0, then it is divisible by 2. if a number ends in 4, then it is divisible by 2. mixed exercises construct an argument draw a valid conclusion from the given statements, if possible. then state whether your conclusion was drawn using the law of detachment or the law of syllogism. if no valid conclusion can be drawn, write no valid conclusion. justify your argument. 18. given: if a figure is a square, then all the sides are congruent. figure abcd is a square. 19. given: if two angles are complementary, the sum of the measures of the angles is 90°. ∠1 and ∠2 are complementary angles. 20. given: ballet dancers like classical music. if you like classical music, then you enjoy the opera. 21. given: if you are an athlete, then you enjoy sports. if you are competitive, then you enjoy sports. 22. given: if a polygon is regular, then all of its sides are congruent. all of the sides of polygon wxyz are congruent. 23. given: if terryl completes a course with a grade of c, then he will not receive credit. if terryl does not receive credit, he will have to take the course again.

Explanation:

12.

Step1: Analyze the statements

The first statement is "If you interview for a job, then you wear a suit." The second is "If you interview for a job, then you will update your resume." There is no common - consequent or antecedent that can be used to form a new conditional statement using the Law of Syllogism.

Step1: Identify the statements

Let \(p\): Tina has a grade - point average of 3.0 or greater, \(q\): Tina is on the honor roll, \(r\): Tina will have her name in the school paper. We have \(p
ightarrow q\) and \(q
ightarrow r\).

Step2: Apply the Law of Syllogism

By the Law of Syllogism, if \(p
ightarrow q\) and \(q
ightarrow r\), then \(p
ightarrow r\).

Step1: Analyze the statements

The first statement is "If two lines are perpendicular, then they intersect to form right angles." The second statement is "Lines \(s\) and \(r\) form right angles." This is an example of affirming the consequent. We cannot draw a valid conclusion using the Law of Detachment or the Law of Syllogism.

Answer:

no valid conclusion

13.