AMSCO'S Geometry. New York - Rye High School

74 LogicApplying Skills17. Let p represent “x is divisible by 2.”Let q represent “x is divisible by 3.”Let r represent “x is divisible by 6.”a. Write the biconditional (p ∧ q) ↔ r in words.b. Show that the biconditional is always true for the domain {2, 3, 5, 6, 8, 9, 11, 12}.c. Do you think that the biconditional is true for all counting numbers? Explain youranswer.18. A gasoline station displays a sign that reads “Open 24 hours a day, Monday throughFriday.”a. On the basis of the information on the sign, is the conditional “The gasoline station isclosed if it is Saturday or Sunday” true?b. On the basis of the information on the sign, is the conditional “If the gasoline station isclosed, it is Saturday or Sunday” true?c. On the basis of the information on the sign, is the biconditional “The gasoline stationis closed if and only if it is Saturday or Sunday” true?d. Marsha arrives at the gasoline station on Monday and finds the station closed. Doesthis contradict the information on the sign?e. Marsha arrives at the gasoline station on Saturday and finds the station open. Doesthis contradict the information on the sign?In 19–22, write a biconditional using the given conditionals and tell whether each biconditional istrue or false.19. If a triangle is isosceles, then it has two congruent sides.If a triangle has two congruent sides then it is isosceles.20. If two angles are both right angles, then they are congruent.If two angles are congruent, then they are both right angles.21. If today is Thursday, then tomorrow is not Saturday.If tomorrow is not Saturday, then today is Thursday.22. If today is not Friday, then tomorrow is not Saturday.If tomorrow is not Saturday, then today is not Friday.2-7 THE LAWS OF LOGICWe frequently want to combine known facts in order to establish the truth ofrelated facts. To do this, we can look for patterns that are frequently used indrawing conclusions. These patterns are called the laws of logic.