Question

{a, e} is the subset of {x: x is a vowel in the English alphabet}. Enter 1 if true or 0 otherwise.

Answer 1

Hint: In this question, we need to determine that the given data {a,e} is the subset of the {x: x is a vowel in the English alphabet} or not. If yes then, the answer is 1 otherwise 0. For this, we will form a set for {x: x is a vowel in the English alphabet} and then verify that {a,e} is the subset or not.

Complete step-by-step answer:
An interval is a set number that consists of all real numbers between a given pair of numbers. An endpoint of an interval is either of the two points that mark the endpoint of a line segment. An interval can be of different types which can include either endpoint or both endpoints or neither endpoint.
An interval that does not include endpoints is an open interval denoted by round brackets (). For closed intervals, they include endpoints of the interval, and they are denoted by square bracket []. Any interval which includes either of the endpoints is denoted by (].
A set is a collection of objects where each object in the set is called an element for that set denoted by \[x \in R\] where x is the element of the set R and a set having no elements to them is called an empty set.
The set for {x: x is a vowel in the English alphabet} can be written as {a,e,i,o,u}. Here, we can see that {a,e} is in the set {a,e,i,o,u} and so we can say that, {a, e} is the subset of {x: x is a vowel in the English alphabet}.
Hence, the given statement is true, and consequently, the answer is 1.

Note: Students often get confused with the terms sub-set as the total values that are included in both the sets, which is not true. Sub-set contains only the common terms which are present in the given sets.