Here we are given that the cardinality of set \(\mathrm{A}\) is 4 and that of a set \(\mathrm{B}\) is 3 .
We must know the meaning of cardinality. It is actually the number of elements that are there in the set. As here we are
given that the cardinality of set \(\mathrm{A}\) is 4 and that of a set \(\mathrm{B}\) is 3 this means that there are 4 elements in the set \(\mathrm{A}\) and there
are 3 elements in the set \(B\).
So we can write it as:
\(n(A)=4\)
\(n(B)=3\)
So we need to find the cardinality of \(A \Delta B\) set.
Let us see through Venn diagram that:
We know that \(A \Delta B\) means all the elements that are there in the set A or the set \(\mathrm{B}\) but not in their intersection or we can
say that all the elements that are there in either set \(\mathrm{A}\) or set \(\mathrm{B}\) nut we don't need to include the elements common to
both the set \(\mathrm{A}\) and \(\mathrm{B}\).
We can write that:
\(n(A \Delta B)=n(A)+n(B)-n(A \cap B)\)
Here we know the values of \(n(A)\) and \(n(B)\) but not the elements that are common to \(\mathrm{A}\) and \(\mathrm{B}\).
Hence we do not know what \(n(A \cap B)\) is. Therefore the value of \(n(A \Delta B)\) cannot be determined.
Hence we can say that \(\mathrm{D}\) ) is the correct option.
Note:
Here in these types of problems we must know all the symbols that are used in the sets related problems. If we are given
the set \((B-A)\) then this would mean that all the elements that are there in set \(\mathrm{B}\) but not in the set \(\mathrm{A}\). These problems
can be easily solved by using the Venn diagram.