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Discrete math
8:23 1. Fill in the blanks using words and a variable or variables to rewrite the given statement: Is there an integer that has a remainder of I when it is divided by 5 and a remainder of 3 when it is divided by 6? Is there an integer n such that n has b Does there exist such that if n is divided by 5, the remainder is 1 and if e There are integers with this property. Can you think of 2. Answer the following questions regarding sets: a Is ? b How many elements are in the set (3,3.2,2,21? e How many elements are in the set 0, 01? a Is (0 0, 103 Is 0 to, 11? 3. Fill in the blanks so that the argument in part (b) has the same logical form as the argument in part (a). a. If all computer programs errors, then this program does not contain an error. contain contains an error. This program Therefore, it is not the case that all computer programs contain crroRS b. If then 2 is not odd Therefore, it is not the case that all prime numbers are odd. 4. Write the statement in symbolic form using the symbols and and the indicated letters to represent the component Billy is a physies major but not a chemistry major. (m a physics major, c-Billy is a chemistry major -Billy is 5. Write the truth table for the statement form: 6. Determine if the two statement forms given below are logically equivalent. Construct a truth table and include a sentence to justify your answer: and
8:23 1 Therefore, it is not the case that all computer programs contain errors b. Ifte 2 is not odd Therefore, it is not the case that all prime mumbers are odd 4. Write the statement in symbolic form using the symbols- and and the indicated letters to represent the component Billy is a physics major but not a chemistry major. (m a physics major, c- Billy is a chemistry major Billy is 5, Write the truth table for the statement form: 6. Determine if the two statement forms given below are legically equivalent. Construct a truth table and include a sentence to justify your answer: and 7. Construct a truth table for the following: 8. Write negations for each of the following statements: a. If today is Family Day, then tomorrow is February b. Ifx is nonnegative, then x is positive or x is e. If n is divisible by 6, then is divisible by 2 and n is divisible 3. 9. Rewrite the statement in if-then form in twe ways, one of which is the contrapositive of the other: Mitch will be allowed in Kazs house only if he is an expert cook Before handing in this assignment, make sure you have provided references for your answers to each question ONL.Yif you used another source other than the textbook as your source of inspiration to answer your gquestion. WHAT TO HANI
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