⊂ A (vi) { , , } ⊂ A (vii) { , , } ∈ A (viii) { , , } ⊂ A (ix) φ ∈ A (x) φ ⊂ A (xi) { φ } ⊂ A . Write down all the subsets of the following sets { a } { a , b } (iii) { , , } (iv) φ . How many elements has P(A), if A = φ ? .
Write the following as intervals : { x : x ∈ R, – < x ≤ } { x : x ∈ R, – < x < – } (iii) { x : x ∈ R, ≤ x < } (iv) { x : x ∈ R, ≤ x ≤ } . Write the following intervals in set-builder form : (– , ) [ , ] (iii) ( , ] (iv) [– , ) . What universal set(s) would you propose for each of the following : The set of right triangles. The set of isosceles triangles.
. Given the sets A = { , , }, B = { , , } and C = { , , , , }, which of the following may be considered as universal set (s) for all the three sets A, B and C { , , , , , , } φ (iii) { , , , , , , , , , , } (iv) { , , , , , , , } . Venn Diagrams Most of the relationships between sets can be represented by means of diagrams which are known as Venn diagrams . Venn diagrams are named after the English logician, John Venn ( - ).
These diagrams consist of rectangles and closed curves usually circles. The universal set is represented usually by a rectangle and its subsets by circles. In Venn diagrams, the elements of the sets are written in their respective circles (Figs . and .
) MATHEMATICS Fig . Illustration In Fig . , U = { , , , ..., } is the universal set of which A = { , , , , } is a subset. Illustration In Fig .
, U = { , , , ..., } is the universal set of which A = { , , , , } and B = { , }