Mathslive.ie

SETS

Exam Cog
①THE SYMBOLS

∩ both   ∪ either   A′ outside

A\B in A not B   #A how many

⊂ subset   ∅ null set { }

②LISTING ELEMENTS
  1. Work out each bracket as a set
  2. Then combine (∩ or ∪)
  3. List once, no repeats
③VENN — TWO SETS

Regions: only A, both (overlap), only B, outside

(A∪B)′ = outside both

★ Fill the overlap first, then work outwards
④NUMBERS IN REGIONS

Every region has a count; they add to #U

(only A) + (both) + (only B) + (neither) = #U

Solve for the unknown.

⑤METHOD
  1. Draw two circles in a box (U)
  2. Put the overlap (both) in first
  3. Fill each region
  4. Add to the total and solve
⑥WATCH-OUTS
⚠ “Both” = the overlap only. “82 use weights” includes the overlap — subtract it for the left-only region.