18)write the negation of the following statements
s: All students study mathematics at the elementary leve
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The negation of the given statement is ~s.thete exists a student who does not study mathematics at the elementary level.
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18)write the negation of the following statements s: All students study mathematics at the elementary level
17)write the negation of the following statements r: All birds have wings
1. (2 points) Write a negation for the following statements: (a) If N is a nonagon, then N is a polygon. (b) If r is divisible by 56, then x is divisible by 7 and r is divisible by 8.
EXERCISES 6 Write and simplify the negation to the following le statements a) 3x<x2+1< 5 W . x>2 Vy<3 6) $9xty >3 .01.29 Izs1. (x-y< L da ih abzc ad bad c) 4x<1e y>2 acd d) a<b<ce bread 2 i) { x=1 Vy <3 e) x+1 <4 K x 2 <24 <3x+S Iz>y>x. f) ab. (cs d & cze) g) { x< 1 v { x=3 • lyce Tyzl
6. (4 marks) Write down the negation of each of the following statements. Then determine whether the statement or its negation is true, and explain why (a) x E R, y E R such that xy 5. (b) z, y E R+ such that V z E Z+, > z.
Discrete Math in the final answer) 6. Write the negation of the following statements (without using (a). Un e Z+, 3p EP, n3 <p < (n + 1)3. (b). Vce R+,3K EZ+, Vn e Z, n > K → n n+100 < c.
16)write the negation of the following statements q: There exists a rational number x such that x2=2
15)write the negation of the following statements i) p: for every real number x,x2>x
Simplify the following sentences in predicate logic so that all the negation symbols are directly in front of a predicate. (For example, Vx ((-0(x)) + (-E(x))) is simplified, because the negation symbols are direct in front of the predicates O and E. However, Væ -(P(2) V E(x)) is not simplified.) (i) -(3x (P(x) 1 (E(x) + S(x)))) (ii) -(Vx (E(x) V (P(x) +-(Sy G(x, y))))) Write a sentence in predicate logic (using the same predicates as above) which is true...
1. In a high school class of 100 students, 42 studied mathematics, 68 studied psychology, 54 studied history, 22 studied both mathematics and history, 25 studied both mathematics and psychology, 7 studied history but niether mathematics nor pychology, 10 studied all three subjects, and 8 took none of these. Randomly selecting a student from the class, what is the probability of the following event that: (a) a person enrolled in psychology takes all three subjects. (b) a person not taking...
1. A mathematics professor believes that the performance of students taking an elementary calculus course has declined in recent years. The professor decides to reuse a final exam that was first administered 10 years ago. At that time the mean score was 81 with s=10, for the 50 students in the section taught by that professor When given to the current class of 53 students, who observed essentially the same set of lectures, the mean is 75 with s=15. If...