Question

State true or false. Correct the statement if it is false.
If \[T = \left\{ {a,l,a,h,b,d,h} \right\}\], then \[n\left( T \right) = 5\].

Answer 1

Hint:
In this question a set \[T\] is given containing certain elements. \[n\left( T \right)\] represents the number of elements in \[T\]. So we have to find the number of elements in \[T\] and find whether it is equal to \[5\] or not.

Complete step by step solution:
A set is a group of well-defined elements. The elements of a set are represented by enclosing them in the second bracket \[\left\{ {} \right\}\], and are separated by “,”.
In the question we are provided with a set \[T\].
\[T = \left\{ {a,l,a,h,b,d,h} \right\}\]
Each term within the second bracket and separated by , are the elements of set \[T\]. So the elements of set \[T\] are \[a,l,a,h,b,d,h\]. Now observe that the elements \[a\] and \[h\] are repeated twice. We know that each element of a set is distinct and repetitions are not considered. Therefore ignoring the repetitions , the elements of set \[T\] are \[a,l,h,b,d\]. Therefore the number of elements in the set \[T\] is equal to \[5\].
Again \[n\left( T \right)\] represents the number of elements in the set \[T\]. It is given that \[n\left( T \right) = 5\], which is correct as we have just verified.

Therefore the given statement is true.

Note:
The representation of a set in the given format i.e. \[\{ a,l,a,h,b,d,h\} \] is known as the roaster form. In this form the order of the elements is immaterial. Sets can also be expressed in the set builder form. Students must be careful while counting the number of elements in the given set. It must also be noted that repetition of elements are not considered i.e. the set \[T = \left\{ {a,l,a,h,b,d,h} \right\}\] is same as the set \[T = \left\{ {a,l,h,b,d} \right\}\].