C3 test
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This document contains 16 logic and critical thinking problems involving statements, truth tables, logic symbols, validity of arguments, and Euler diagrams. The problems cover topics such as determining logical equivalence, constructing and analyzing truth tables, identifying inverse, converse and contrapositive statements, and determining the validity of arguments using logic rules or diagrams.
C3 test
- 1. 1) Write the statement in words given: p: I am happy q: I am hungry r: I am tired. ~r ∧ (p --> ~q) 2) Write the statement in symbols given: r = "The puppy is trained." p = "The puppy behaves well." q = "the owners are happy." "If the owners are happy, then the puppy is trained and behaves well." 3) Construct a truth table for the statement. q V ~(p ↔ r) p q r ... TTT TTF TF T TF F F TT F TF F F T F F F 4) Construct a truth table for the statement: ~p → (p V q) p q TT TF F T F F
- 2. 5) Construct a truth table for the statement. ~p ∧ (~q→ r) p q r TTT TTF TF T TF F F TT F TF F F T F F F 6) Determine which, if any, of the three statements are equivalent. I) If tomorrow is Monday, then today is Sunday. II) If tomorrow is not Monday, then today is not Sunday. III) It is false that today is Sunday and tomorrow is Monday 7) Use DeMorgan's laws or a truth table to determine which statements is equivalent to: ~(p ∧ ~q), 1. ~p ∧ ~q 2. ~p V ~q 3. ~p ∧ q 4. ~p V q 8) Determine which, if any, of the three statements are equivalent. I) If it is sunny, then I will go swimming. II) If I do not go swimming, then it is not sunny. III) If it is sunny and I will go swimming.
- 3. 9) Write the inverse, converse, and contrapositive to the statement below. Clearly label each statement (ie - inverse: ...., contra:...., etc) If we will start a campfire, then we will roast marshmallows. 10) Use the logic laws to tell whether the argument is valid or invalid. Use True for Valid and False for Invalid. p→q ~p _____ ∴ ~q 11) Use the logic laws to state whether the argument is valid or invalid. Use True for Valid and False for Valid. p→q ~q _____ ∴ ~p 12) Use the logic laws to state whether the argument is valid or invalid. Use True for Valid and False for Valid. p∨q ~q _____ ∴p 13) Use the logic laws to state whether the argument is valid or invalid. Use True for Valid and False for Valid. p→q ~q → ~r _____ ∴r
- 4. 14) Use an Euler Diagram to tell if the argument is valid or invalid. Use True for Valid and False for Invalid. All computers are electric powered machines. Some electric powered machines are expensive Therefore, my computer is expensive. 15) Use an Euler Diagram to tell if the argument is valid or invalid. Use True for Valid and False for Invalid. All food is good for you. Cupcakes are a food. Therefore, cupcakes are good for you. es 16) Extra Credit: Write a statement for the circuit and create a truth table to find when the light is on. p q s TTT TTF TF T TF F F TT F TF F F T F F F
- 5. Answer: