Problem 1 (10 pts] (5pts each): Logical Equivalence Use the laws of logical equivalence to simplify these logical statem

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Problem 1 10 Pts 5pts Each Logical Equivalence Use The Laws Of Logical Equivalence To Simplify These Logical Statem 1 (213.73 KiB) Viewed 40 times

Problem 1 (10 pts] (5pts each): Logical Equivalence Use the laws of logical equivalence to simplify these logical statements. To fully simplify the expression, eliminate all implications and make sure negations are directly in front of single propo- sitions wherever negations occur. State the equivalence law you are applying with each step. i. -(-(p+q) +9) ii. -(p1q) + (p1-9) A Problem 2 [10 pts]: Circular Argument Find all truth value combinations for a, b, c, d that satisfy (a + b)^(b + c)^(c+d)^(d + a), without using a truth table. (Reason it out logically and explain your reasoning!) Problem 3 [10 pts]: Where is Spock when you need him? As Captain of the USS Enterprise, your mission is to travel at warp speed to the planet Zorg to rescue some Vulcans whose vessel recently crashed. But beware – Romulan spies may be trying to infiltrate your ship! When you arrive, you find three aliens named Aravik, Balev, Chu'lak. They offer up the following statements: • Aravik: Chu'lak is not a Romulan • Balev: Either Chu'lak is a Romulan or I am a Vulcan. • Chu'lak: Balev is a Romulan. Knowing as you do that Vulcans always tell the truth and Romulans always lie, which of the aliens, if any, do you rescue and which do you leave stranded on the planet? Be sure to show how you came to your conclusion! Hint: The most direct approach is to create a truth-table that enumerates each possibility, and then rule how any scenarios where a Vulcan is lying or a Romulan is telling the truth.