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web.groovymark@gmail.com
- November 9, 2024
Question 41
What does the term “predicate” indicate in logic?
a) A constant value
b) A logical statement that can be true or false based on variable values
c) A defined set of elements
d) An unconditional statement
Correct Answer: b) A logical statement that can be true or false based on variable values
Explanation: A predicate is a statement that contains variables and becomes a proposition when specific values are assigned, determining its truth value.
Question 42
What does a relation being transitive imply?
a) Every element relates to itself
b) If xRy and yRz, then xRz must hold
c) It is symmetric
d) It has no elements
Correct Answer: b) If xRy and yRz, then xRz must hold
Explanation: A transitive relation asserts that if one element is related to a second, which in turn is related to a third, then the first element must also relate to the third.
Question 43
What does the operation A∩(B∪C) simplify to?
a) A∩B∪A∩C
b) A∪B∩C
c) A∩B∩C
d) None of the above
Correct Answer: a) A∩B∪A∩C
Explanation: This expression exemplifies the distributive property of set operations, distributing the intersection over the union.
Question 44
What is the implication of finding a counterexample in logic?
a) It supports the claim
b) It disproves the statement
c) It proves the statement
d) It validates the hypothesis
Correct Answer: b) It disproves the statement
Explanation: A counterexample serves as evidence that a general statement or claim is false, thereby disproving the assertion being examined.
Question 45
What does it mean for two sets to be pairwise disjoint?
a) They share at least one element
b) They have no elements in common for every pair of sets in the sequence
c) They can have some overlapping elements
d) They are identical
Correct Answer: b) They have no elements in common for every pair of sets in the sequence
Explanation: Pairwise disjoint sets are those where any two distinct sets in the collection do not share any elements, ensuring complete separation.
Question 46
Which of the following laws states that p∨F = p?
a) Domination Law
b) Identity Law
c) Idempotent Law
d) Complement Law
Correct Answer: b) Identity Law
Explanation: The identity law in Boolean algebra states that combining a variable with the identity element of OR, which is false (F), results in the original variable.
Question 47
What does the term “domain” refer to in a function?
a) The set of all possible outputs
b) The set of all inputs
c) The total elements in a function
d) The average value of outputs
Correct Answer: b) The set of all inputs
Explanation: The domain of a function consists of all possible input values for which the function is defined, determining what elements can be processed.
Question 48
What does the notation p→q represent?
a) p and q are equivalent
b) If p is true, then q is also true
c) p and q are unrelated
d) p must be false
Correct Answer: b) If p is true, then q is also true
Explanation: The expression p→q denotes a conditional relationship where the truth of q depends on the truth of p.
Question 49
What is the significance of the double complement law?
a) It demonstrates that a variable can change
b) It shows that a double negation returns the original variable
c) It establishes that variables must be equal
d) It provides an example of a contradiction
Correct Answer: b) It shows that a double negation returns the original variable
Explanation: The double complement law states that negating a variable twice yields the original variable, facilitating simplification in Boolean expressions.
Question 50
In graph theory, what defines a path?
a) A sequence of edges without any restrictions
b) A walk where no vertices are repeated
c) A closed walk
d) A trail that can repeat edges
Correct Answer: b) A walk where no vertices are repeated
Explanation: A path is defined as a traversal that does not allow for repeated vertices, ensuring that each vertex is visited only once.
