CSCI 190 Exam I Practice
1)
a)Write the contrapositive of the following conditional statement
If it is raining, then the streets are wet.
b) Write the negation of the following:
Some Mt. SAC students are international students.
c)Express the following argument symbolically and determine if it is valid: If I study hard, then I get A’s or I get rich. I don’t get A’s and I don’t get rich. Therefore I didn’t study hard.
2)
Prove or disprove each of the following:
a)For the domain of real numbers,
b)For the domain of integers,
3)Prove that is odd if and only if is even.
4)Prove that if , then (hint: first pick . You need to show )
5)Prove that there is no largest integer.
6)
a)Show is
b)Show is not
7) Compute the Boolean Product for and
8)
a)Sketch for x in
b)Show defined as is onto. Justify your answer.
9) Find the close form (non-recursive form)of the recursive sequence ,
10)(2 points each: true/false, short answers: No partial credit points will be given. You are not required to show work.)
a)True/False: Let A, B be sets. If , then
b)True/False: for all real numbers x (including negatives)
c)True/False: Determine if the following statement is true or false: if and only if
d)Is the set of rational numbers countable or uncountable? ______
e)Is the set of real numbers countable or uncountable? ______
f)Rewrite the following sentence in “If P then Q” form. I pass CSCI 190 only if I study 10 hours a week.
______
g)Find the power set of ______
h)Find where ______
i)Compute ______
j)Find the nth term of the sequence ______
k)For defined by find and
l)Let A, B be matrices with C=AB. Find an expression for (using ) given
______
11)Prove if and , then for nonzero integers a,b,c.
12)Show is
13)
a)(1 point) True/False:
b)(1 point) True/False:
c)(2 points) Find the power set of
d)(2 points) For and , find
14)Find a non-recursive expression for
15)Determine if defined by is onto.
16)Prove that is logically equivalent to
17)Prove that if Prove that if , then for nonzero integers a,b,c.
18)Prove or disprove the following:
, where the domain is the set of all natural numbers 1, 2, 3, ….
19)Construct a truth table to determine if
20)Show that if then
21)Suppose x is a nonzero real number. Prove that if is an irrational number, then is also an irrational number.
22)Prove or disprove:
a)For the domain of real number
b)For the domain of real numbers,
23)Prove that there is no positive integer satisfying
24)(2 points each) Do NOT show work.
a)True/False
b)Write the negation of . Make sure the negation appears next to p(x,y)
c)Find an integer such that ______
d)For defined by , compute
e)Negate the following sentence: Nancy is tall and beautiful.
f)=______
g)What conclusion if any can be drawn from the following: If there is gas in the car, then I will not drink beer. If I drink beer, then I will go shopping. I did not go shopping.
h)For defined by , find
25)
a)(7 points) Find a formula (in closed form) for the recursive sequence
b)(3 points) Find the nth term of the sequence
26)Prove or disprove: , where the domain is the set of all real numbers.
27)Prove or disprove: defined by is a bijection.
28)For a function defined by , find a) b)
29)Prove that is irrational.
30)If is even, then is even or is even.
31)
a)Show
b)Show
c)Show
32)Prove that if , then for integers a,b,