7/29/2019 MAD111 Review Chap 1 2 ENG
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MAD111 - Review Chapter 1 + 2
1. How many tuples of (p, q, r) are there thatmake the compound
proposition
( )p q r true?
A. 2 B. 4 C. 6 D. None
2. Compute
(11011 01101) (01010 11011) .
A. 10101 B. 01010 C. 11111 D. None
3. The compound propositions( ) ( )p r q r and ( )p q r are
logically equavalent ?
A. Yes B. No
4. Given the propositional function P(x) on
the domain { -1, 0, 1}. Express the statement
(( 0) ( ))x x P x without using quantifiers.
A. ( 1) (0) (1)P P P B. (0) (1)P P
C. ( 1) ( (0) (1))P P P D. None
5. Let L(x,y) be the statement x loves y.Translate the statement
An loves anybody
except one person into logical expression.
A. )),(( xAnLx
B.))),()((),(( yAnLxyyxAnLx
C.))),()((),(( yAnLxyyxAnLx
D.))),()((),(( yAnLxyyxAnLx
6. Express the negation of
( ( , ) ( ( , ) ( , )))x y P x y y Q x y R x y
so that no negation precedes a quantifier.
A. ( ( , ) ( ( , ) ( , )))x y P x y y Q x y R x y
B. ( ( , ) ( ( , ) ( , )))x y P x y y Q x y R x y
C. ( ( , ) ( ( , ) ( , )))x y P x y y Q x y R x y
D. None
7. Given the hypotheses
-If Quang does every exercise in thisbook then Quang gets an A
in this class.
- If Quang gets an A in this class then
Quang gets an A on the final exam.- Quang gets an A in this
class.
What conclusion can be drawn ?
A. Quang does every exercise in this book,Quang gets an A in
this class and Quang
gets an A in this class.
B. Quang does every exercise in this bookand Quang gets an A on
the final exam.
C. Quang gets an A on the final exam and
Quang gets an A in this class.
D. Quang gets an A in this class and Quanggets an A on the final
exam.
E. None
8. Which statements are false ?
A. { } B. P({1})
C. {1} D. None
9. Find the cardinality of the set({ , { }, 1, {1, 2}}) {x,{a,
b}, x}P
A. 32 B. 12 C. 48 D. None
10. Let U = {1, 2, , 10} be an universal
set. Represent the subset A={2, 3, 5, 7} as abit string of
length 10, where the i-th bit is 1
if i belongs to A and is 0 if i does not belongto A.
A. 1111000000 B. 0110110000C. 0101011000. D. None
7/29/2019 MAD111 Review Chap 1 2 ENG
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11. Compute 2.5 3.5 2.5 3.5 .
A. -2 B. -1 C. 0 D. None12. Which functions from the set of
integers
to itself are not one-to-one?
A. f(n) = n3 B. ( ) / 2 / 2f n n n= +
C. ( ) / 2 .f n n n= D. None
13. Which functions from the set of integers
to itself are onto?
A. f(n) = n3 B. ( ) / 2 / 2f n n n= +
C. ( ) / 2 .f n n n= D. None
14. Let f(x) = x2
4; g(x) = x + 2. Find thecomposition ( )f g xo .
A. x2 + x - 2 B. x2 2
C. x2 + 4x D. None15. Given the sequence:1, 2, 2, 2, 3, 3, 3, 3,
3,
Find the 100th term of the sequence.
A. 10 B. 20 C. 21 D. 50
16. Find:
10
1
2 ( 1)i i
i =
+
A. 211-1 B. 211-2
C.111 ( 2)
11 ( 2)
D. None
