Question 1 |
Consider the following statements:
S1: The sum of two singular nxn matrices may be non-singular
S2: The sum of two nxn non-singular matrices may be singular.
Which of the following statements is correct?
S1: The sum of two singular nxn matrices may be non-singular
S2: The sum of two nxn non-singular matrices may be singular.
Which of the following statements is correct?
S1 and S2 are both true | |
S1 is true, S2 is false | |
S1 is false, S2 is true | |
S1 and S2 are both false |
Question 1 Explanation:
Question 2 |
Consider the following relations:
R1(a,b) iff (a+b) is even over the set of integers
R2(a,b) iff (a+b) is odd over the set of integers
R3(a,b) iff a.b > 0 over the set of non-zero rational numbers
R4(a,b) iff |a - b| <= 2 over the set of natural numbers
Which of the following statements is correct?R1 and R2 are equivalence relations, R3 and R4 are not | |
R1 and R3 are equivalence relations, R2 and R4 are not | |
R1 and R4 are equivalence relations, R2 and R3 are not | |
R1, R2, R3 and R4 are all equivalence relations |
Question 2 Explanation:
Question 3 |
Consider two well-formed formulas in prepositional logic.
F1: \; P\Rightarrow \neg P
F2: \;( P\Rightarrow \neg P)\vee ( \neg P\Rightarrow P)
Which of the following statements is correct?
F1: \; P\Rightarrow \neg P
F2: \;( P\Rightarrow \neg P)\vee ( \neg P\Rightarrow P)
Which of the following statements is correct?
F1 is satisfiable, F2 is valid | |
F1 unsatisfiable, F2 is satisfiable | |
F1 is unsatisfiable, F2 is valid | |
F1 and F2 are both satisfiable |
Question 3 Explanation:
Question 4 |
Consider the following two statements :
S1: {0^{2n}|n\geq 1|} is a regular language
S2 : {0^{m}1^{n}0^{m+n}|m\geq 1 and n\geq 1|} is a regular language
Which of the following statements is correct?
S1: {0^{2n}|n\geq 1|} is a regular language
S2 : {0^{m}1^{n}0^{m+n}|m\geq 1 and n\geq 1|} is a regular language
Which of the following statements is correct?
Only S1 is correct | |
Only S2 is correct | |
Both S1 and S2 are correct | |
None of S1 and S2 is correct |
Question 4 Explanation:
Question 5 |
Which of the following statements true ?
If a language is context free it can be always be accepted by a deterministic
push-down automaton. | |
The union of two context free language is context free. | |
The intersection of two context free language is context free | |
The complement of a context free language is context free |
Question 5 Explanation:
There are 5 questions to complete.