WASSCE SHS
A set is a collection of distinct objects. Union joins two sets. Intersection keeps only what they share.
List elements in braces, and do not repeat an element inside one set. The union of A and B, written A ∪ B, contains every element that is in A or in B or in both. The intersection, A ∩ B, contains only the elements that are in both. The number of elements in A is n(A). For finite sets, n(A ∪ B) = n(A) + n(B) − n(A ∩ B). The subtraction stops you counting the overlap twice. A Venn diagram is the picture of the same fact: the overlap is the intersection.
The universal set is everything under discussion. An element outside A but inside the universal set is in the complement of A. Read the words carefully. "Neither" is outside both sets. "Both" is the intersection. "Either, or both" is the union. Translating the English into the symbol before you calculate is the step that keeps the algebra honest.
Listing is enough when the question says list. Counting is enough when it asks for the number. Do not do the other one and stop, if the question asked for both. The formula for the union needs the intersection subtracted. Forgetting that subtraction double counts, and the number comes out too big. Elements must belong to the universal set the question gave. Inventing 9 when the universal set stops at 8 scores nothing.
These are practice questions in the style of the paper, with a model answer and a mark scheme. They are not a promise of what your paper will ask.
4 marks
The universal set is {1, 2, 3, 4, 5, 6, 7, 8}. A = {1, 2, 3, 4} and B = {2, 4, 6, 8}.
(a) List A ∩ B. (1 mark)
(b) List A ∪ B. (2 marks)
(c) Find n(A ∪ B). (1 mark)
(a) {2, 4}
(b) {1, 2, 3, 4, 6, 8}
(c) 6
2 marks
n(A) = 12, n(B) = 9 and n(A ∩ B) = 4. Find n(A ∪ B). (2 marks)
n(A ∪ B) = 12 + 9 − 4 = 17.
1 mark
In the sets above, which of 1, 2 and 7 lie in neither A nor B? (1 mark)
7. The number 1 is in A, and 2 is in both.
More questions on this topic are inside GLearn, marked as you answer, with the reason written out. The first ones need no account.
Practise Core Mathematics freeThe union is everything in either set. The intersection is only what is in both. If A is {1, 2, 3, 4} and B is {2, 4, 6, 8}, the intersection is {2, 4} and the union has six elements.
The elements in both sets were counted in n(A) and again in n(B). Subtracting n(A ∩ B) once removes that double count. 12 + 9 − 4 = 17, not 21. All WASSCE Core Mathematics past questions