Which of the following is NOT a condition for a topology on a set $X$?

C. Intersection of any open sets is open

A. The empty set and $X$ are open

B. Union of any collection of open sets is open

C. Intersection of any open sets is open

D. Intersection of finitely many open sets is open

A disjunction of two statements $p$ and $q$ is false if?

C. $p$ is true and $q$ is false

D. at least one of $p$ or $q$ is true

B. at least one of $p$ or $q$ is true

C. exactly one of $p$ or $q$ is true

Mathematics · Sets & Functions · page 8 of 8

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71.
Which of the following is NOT a condition for a topology on a set $X$?
Correct Answer: C. Intersection of any open sets is open
One-liner
In a topology, the intersection of finitely many open sets is open, not the intersection of any collection of open sets.
72.
A disjunction of two statements $p$ and $q$ is false if?
Correct Answer: A. both $p$ and $q$ are false
One-liner
The disjunction $p \lor q$ is false only when both $p$ and $q$ are false.
73.
A conjunction of two statements $p$ and $q$ is true only if:
Correct Answer: A. both $p$ and $q$ are true
One-liner
The conjunction $p \land q$ is true only when both $p$ and $q$ are true.
74.
The set of natural numbers along with $0$ is called?
Correct Answer: D. Whole numbers
One-liner
The set of natural numbers together with $0$ is called the set of whole numbers.
75.
If two sets $A$ and $B$ do not have a common element, they are called?
Correct Answer: D. Disjoint sets
One-liner
Two sets with no common element are called disjoint sets.