Name Spring 2018 Math 231 Date 3.2 Predicates and Quantified Statement II 1. Whi
ID: 3195551 • Letter: N
Question
Name Spring 2018 Math 231 Date 3.2 Predicates and Quantified Statement II 1. Which of the following is a negation for all dogs are loyal More than on answer may correct a, All dogs are disloyal No dogs are loyal. Some dogs are disloyal. c. d. Some dogs are loyal. There is a disloyal animal that is not a dog e. f. There is a dog that is disloyal. g. h. No animals that are not dogs are loyal. Some animals that are not dogs are loyal. 2. Write a negation for " a band B such that B has won at least 10 Grammy awards 3. Write negations for each of the following statements a. Vx cR, ifx (x+1) 0, then x 0 or x-1 V integers d, if 6/d is an integer then d 3. V integers n, if n is divisible by 6, then n is divisible by 2 and n is divisible by 3. If a function is differentiable, then it is continuous. b. c. d. 4. Write converse, inverse and contrapositive for each of the following statements: a. V real numbers x, if 1 0 b. vn eZ, if" is prime then n is odd or n = 2. Rewrite each statement without using the word necessary or sufficient. a. Being divisible by 8 is a sufficient condition for being divisible by 4. b. Passing a comprehensive exam is a necessary condition for obtaining a master's d c. Being a polynomial is not a sufficient condition for a function to have a root. 5. d. Having a large income is not a necessary condition for a person to be happyExplanation / Answer
Ans
1) a) All dogs are disloyal b) No dogs are loyal
2) € a band B who lost all 10 Grammy awards.
3) a) x is less than zero and x is greater than -1 .
b) For all integers d , if 6 /d is non integer than d is not equal to 3 .
c) For integers n , if n is multiple of 6 then n is multiple of 2 and n is a multiple of 3.
d) If a function is not continuous then it should not be differentiable.
4)a) For all real numbers if x is greater and equal to zero and less than one than x +1 is less than zero.
b) For n € Z ,if n us non prime then n is even or n=3.
5)a ) Being divisible by 8 is also divisible by 4.
b) To obtain a master degree you can to pass a comprehensive exam.
C) Being a polynomial is a condition for a function to have a root.
D) Having a large income is a condition to be happy.
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