4. Write each statement in symbolic form, and use truth tables to determine if they are logically equivalent: (define any variables you use) A: If you study hard and do all homework, then you will pass the class. B: If you study hard and did not pass the class, then you did not do all your homework.

8. Write the negation of each statement as simply as possible: (a) If it rains, then it is cold. (b) He swims if and only if the water is warm. (c) If it snows, then they do not drive the car.

Let  p = Sam owns a sedan.        q = Joan owns an SUV.        Translate the following statement into symbols.  Then determine under what conditions the compound statement is true.  Note:  A truth table may be needed.        Sam does not own a sedan, but Joan does not own a SUV.

Alice and Belle are perfect logicians. Each of them is given a different fraction, of the form , where n is a positive integer. They only know their own number and they know it's a different fraction from the other. They need to tell whose number is larger. The following conversation occurs: Alice: "I don't know". Belle: "I don't know either." Alice: "I still don't know." Belle: “Now I know whose number is larger." Alice: "Now I know your number too." Who has the larger number? What is the difference of the denominators? (A) Alice. 1. (B) Alice. 2. (C) Belle. 1. (D) Belle. 2.