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To find the cardinality of A, we count the number of elements in the set, which is 4.
To find the cardinality of B, we count the number of elements in the set, which is 6.
To find the cardinality of AUB, we combine all the elements in both sets and remove any duplicates, giving us a total of 8 elements.
To better visualize the relationship between A and B, we can draw a Venn diagram. We can draw two overlapping circles, one for each set, with the shared element "a" in the middle. Set A includes the elements "m", "t", and "h", which are represented outside of the B circle. Set B includes the elements "g", "r", "p", "h", and "s", which are represented outside of the A circle. The intersection or overlap of the two circles represents the shared element "a".
Step-by-step explanation:
The cardinality of an event refers to the number of elements or outcomes in that particular event.
For the first set, A = {m, a, t, h}, the cardinality is 4 because there are 4 elements in the set.
For the second set, B = {g, r, a, p, h, s}, the cardinality is 6 because there are 6 elements in the set.
The union of two sets refers to the combination of all the elements present in both sets without any duplication. The cardinality of AUB, or the union of sets A and B, is therefore 8 because there are 8 unique elements between the two sets.
To draw a Venn diagram to illustrate AUB, we can draw two overlapping circles, one that represents set A and another that represents set B. The shared element “a” can be placed in the region where the two circles overlap. The elements that belong only to set A, {m, t, h}, can be placed within the circle representing A, but outside the circle representing B. The elements that belong only to set B, {g, r, p, s}, can be placed within the circle representing B, but outside the circle representing A. This Venn diagram should help to visualize how the elements of the two sets combine to form the set AUB.
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