Search & Filtering
1. Suppose that f is defined recursively by:
f (0) 5= and f n( + =1) 2fn+5. Find f(1), f(2), f(3) and f(4)?
In the following argument, determine the validity or otherwise of the
Statement:
a) “If you aren’t polite, you won’t be treated with respect. You aren’t
treated with respect. Therefore, you aren’t polite.
b) “If you play football during a thunderstorm, you’ll get hit by lightning.
You didn’t get hit by lightning. Therefore, you didn’t play football in a
thunderstorm”
Therefore, taxes are lowered.”
(i) Write out the propositional statements in the above argument?
(ii) State the premise(s) and conclusion in the argument?
(iii) Using a truth table, determine the validity of the argument?
Let f be a function from Z to R, such that f(x)=x/10, then f is
a) an increasing function
b) a strictly increasing function
c) a decreasing function
d) an onto function
Find f∘g and g∘f , where f(x)=x^2+2x+1 and g(x)=x^2-20, are functions from R to R.
Type/Insert your answer here!
i) Let S={2,4,7} and T={1,3,5}. Find f(S×T) if
f(x,y)=⌊14x/3y⌋
Type/Insert your answer here!
Note: No partial credit would be admissible in this question
f(x,y)=x^2+y^3
Type/Insert your answer here!
Note: No partial credit would be admissible in this question
3)Let x=n+ε, where n is an integer and 0≤ε<1. If ⌊55x/7⌋=8n, then which of the following cannot be a value of x:
a) 14.3
b) 37.7
c) 46.9
d) 51.6
4) Let x=n+ε, where n is an integer and 0≤ε<1. If ⌈33x/8⌉=5n, then which of the following is a valid value of x:
a) 5.8
b) 4.7
c) 6.1
d) 2.5
Let f be a function from the set A to the set B. Let S and T be two disjoint subsets of A (i.e S∩T=∅); then which of the following cannot be true:
a) if f is invertible, then f(S)∩f(T)=∅
b) if f(S)∩f(T)≠∅, then f is a one-to-one function
c) if f(S)∪f(T)⊆B, then f is an onto function
d) none of the above
Express the following using language of Predicate Calculus, where it is understood that the people being discussed are in the courtroom. If any sentence is ambiguous, give all symbolic versions. (i) All judges are sober (ii) There is a dishonest lawyer. (iii) All defendants are innocent. (iv) Some plaintiffs are lawyers (v) Anybody who is honest and a defendant is innocent (vi) All defendants who are not sober are dishonest.
Express the following using language of Predicate Calculus, where it is understood that the people being discussed are in the courtroom. If any sentence is ambiguous, give all symbolic versions. (i) All judges are sober (ii) There is a dishonest lawyer. (iii) All defendants are innocent. (iv) Some plaintiffs are lawyers (v) Anybody who is honest and a defendant is innocent (vi) All defendants who are not sober are dishonest
Let R be the relation on the set A {1,2,3,4,5,6,7} defined by the rule (a,b) elements of R if the integer product of (a,b) is divisible by 4. List the elements of R and its inverse?
