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# Theo Pre-Test 1b

### Theo Pre-Test 1b ****Not Populating Correctly go to CRAM****

Term | Definition |
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Several forms of negation are given for each statement. Which are correct if any? a. The carton is sealed or the milk is sour. 1. The milk is not sour or the carton is not sealed. 2. The carton is not sealed and also the milk is not sour. 3. If th | ? |

Construct a truth table for the given compound proposition. Use one column in truth table for exactly one operation. Remember about order of precedence!!! q⇿p ⨁ p∧q → qVq’ p q ... ... ... T T____ ____ _____ T F ____ ____ _____ F T__ | ? |

Which rule of inference is used in each argument below? Alice is a Math major. Therefore, Alice is either a Math major or a CSI major. Jerry is a Math major and a CSI major. Therefore, Jerry is a Math major. If it is rainy, then the pool will be cl | ? |

You are given proof sequence. Justify each step in it (meaning, write down what rule was used to derive it, and from which previously obtained step(s) if applies). Argument is: (s’ ∧ c) ∧ (w → s) ∧ (w’ → t) ∧ (t → h)→ h Proof sequence (you should subs | ? |

Use propositional logic to prove the following argument is valid. Use the capital letters I, H, F to define the propositions. “If interest rates drop, the housing market will improve. Either the federal discount rate will drop, or the housing market will | ? |

Let Q(x) be the statement “x+1≤2x”. If the domain consists of all integers, what are the truth values of the following statements? Explain your answers. (a) Q(1) (b) Q(-5) (c) ∀x Q(x) (d) ∃x Q(x) (e) ∃x (Q(x))’ | ? |

Let C(x,y) mean that student x is enrolled in class y, where the domain for x consists of all students in your school and the domain for y consists of all classes being given at your school. Express each of these statements by a simple English sentence | ? |

Domain is all creatures, and predicates defined as follows: C(x) = “x is a cat.” D(x) = “x is a dog.” S(x) = “x is a celebrity.” L(x,y) = “x likes y.” Translate into predicate logic (use quantifiers ∃, ∀ where necessary ): 1. “Tom Brady is a celebri | ? |