Search & Filtering
Show that ¬ (P Q) (P V Q) Λ ¬(P Λ Q) (P Λ ¬Q) V (¬ P Λ Q) without using truth table
Show that the relation p = {(a,b) | a -b is an integer} on the set of real numbers R is equivalence relation
i) Which type of relation is shown in below expression
R1 = { (a,b) | a = b }
Find each of the function below, indicate whether the function in onto, on-to-one neither or both. If the function is not onto or nor one-to-one, give an example showing why
G;R R. g(x)=x^3
- A debating team consists of three boys and two girls. Find the number n of ways they can sit in a row if the boys and girls are each to sit together.
Given R = (0^*10^+)^+1^*(0∗10+)+1∗ and S =(1^*01^+)^*(1∗01+)∗
.
a) Give an example of a string that is neither in the language of R nor in S. [2marks]
b) Give an example of a string that is in the language of S but not R. [2 marks]
c) Give an example of a string that is in the language of R but not S. [2 marks]
d) Give an example of a string that is in the language of R and S. [2 marks]
e) Design a regular expression that accepts the language of all binary strings with no occurrences of bab [4 marks]
Prove the following statement by induction. For all nonnegative integers nn, 3 divides n^3 +2n +3n. State the mathematical induction and show your work clearly.
An examination paper consists of 5 questions in section A and 5 questions in section B. A total of 8 questions must be answered. In how many ways can a student select the questions if he is to answer at least 4 questions from section A.
Find each of the function below, indicate whether the function in onto, on-to-one neither or both. If the function is not onto or nor one-to-one, give an example showing why
.
H;Z Z. h(x)=x^3
Find each of the function below, indicate whether the function in onto, on-to-one neither or both. If the function is not onto or nor one-to-one, give an example showing why
.
G;R R. g(x)=x^3
