# Math for Computer science Questions and Answers 171 to 180

## Math for Computer science

### Questions  171 to 180

171.
What is the correct sequence of logical operators?
 (a) ¬, ∧, ∨, → ,  ↔ (b) ¬,  ∨,∧, → ,  ↔ (c) ¬,  →, ↔, ∨,∧ (d) ∧, ∨, → ,  ↔,¬ (e) ¬, ∧, ∨,  ↔, →.
172.
Kangaroos live in Australia and are marsupials. Therefore kangaroo is a marsupial.
Which rule of inference is used in the above argument?
 (a) Addition (b) Simplification (c) Modus ponens (d) Modus tollens (e) Resolution.
173.
Identify the missing values from the below truth table.
 P Q (P ÅQ) F F F T T F T T T F

 (a) T,T (b) T,F (c) F,F (d) F,T (e) Cannot be determined.
174.
Let P be the proposition "It is snowing",
Q  be the proposition "I will go the beach", and
R be the proposition "I have time".
Which of the following is the logical equivalent of the English sentence
"If it is not snowing and I have time, then I will go to the beach".
 (a) (P∧ Q) → R (b) (P∨ Q) → R (c) (¬P∧ R) → Q (d) (¬P∨ Q) → R (e) (¬P∨ Q) ↔ R.
175.
A coin is tossed and a single 6-sided die is rolled. Find the probability of landing the head side of the coin and rolling a 3 on the die.
 (a) 1/2 (b) 1/12 (c) 1/3 (d) 1/6 (e) 2/3.
176.
A composite integer n that satisfies the congruence for all positive integers b with gcd(b,n) = 1 is called a Carmichael number.
 (a) bn–1 ≡ 1 (mod n) (b) bn ≡ 1 (mod n) (c) bn–1 ≡ b(mod n) (d) bn+1 ≡ 1 (mod n) (e) bn–1 ≡ 1 (mod n+1).
177.
In a group of 20 people 18 like pink color and 7 like green color. How many people like both the colors?
 (a) 3 (b) 4 (c) 5 (d) 7 (e) 11
178.
Suppose a coin is flipped three times. Let X(t) be the random variable that equals the number of tails that appears when t is the outcome. Then X (HTT) is
 (a) 3 (b) 2 (c) 1 (d) 0 (e) 4
179.
a= (1011)2 and b= (1010)2, a + b = ?
 (a) 11111 (b) 10001 (c) 10101 (d) 10011 (e) 10111
180.
In a survey out of 50 people, 18 watch cricket, 28 watch Olympics and 7 people watch none. Find how many people watch both the games.
 (a) 5 (b) 8 (c) 3 (d) 12 (e) 9

#### Answers

 171 Answer : (a) Reason:  by the order of precedence. 172 Answer : (b) Reason:  p: Kangaroos live in Australia q: Kangaroos are marsupials hypoyhesis : p∧q by simplification conclusion is q. 173 Answer : (d) Reason:  By the truth table of P ÅQ 174 Answer : (c) Reason:  by the procedure of translation of English into logical equivalent form 175 Answer : (b) Reason:  Probability of getting head is ½ Probability of getting 3 is 1/6 Probability of occurring both is 1/12. 176 Answer : (a) Reason:  by the definition of  Carmichael number. 177 Answer : (c) Reason:  by principle of inclusion- exclusion 18+7-20=5 178 Answer : (b) Reason:  by the random variable  definition X(HTT) = __2___. 179 Answer : (c) Reason:  by the binary sum 1011+1010 = 10101 180 Answer : (c) Reason:  by the principle of inclusion- exclusion  18+28-43=3

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