Season 1 • Episode AP06 • Sets and relations 0Sets and relations

Season 1Episode AP06

Time frame 55 mins

Objectives :• Introdu e the on ept of sets and relations.• Introdu e the main operations on sets : union, interse tion and omplement.• Introdu e the symbols ∈, 6∈, ⊂, 6⊂, ∪, ∩.• Use of Venn diagramMaterials :• 1 opy per student of the exer ise sheet.• Slideshow.1 – Definitions 10 minsUsing a slideshow, the tea her introdu e the main on epts.2 – Exercises remaining timeA exer ise sheet is handet out to the students.

Sets and relationsSeason 1Episode AP06

Document 55 mins

Sets and memberships1. Let Ω be an universe, A and B two subsets of Ω. Des ribe A, A ∩ B and A ∪ Bwhen :(a) Ω = 1; 2; 3; 4; 5; 6;A = 1; 5; 6 and B = 2; 5.(b) Ω=blue ;white ;red ;yellow ; A =blue ;yellow and B =red.( ) Ω = a; b; c; d; e; f ; g;A = a; b; f ; g; e and B = b; c; d.2. Let A = b; r; a; v; o and B = t; r; i; o.Fill out the blanks with the symbols =,∈, 6∈,⊂, 6⊂ :(a) a . . . A(b) t; r; a . . .B( ) r . . . A ∩B(d) r; i . . .A ∩ B(e) r; i . . .A ∩ B

(f) s . . .A ∪ B(g) b; r; a; v; o . . .A ∪ B(h) i . . . A ∩B(i) b; a; t; i; v; o; r . . .A ∪B3. We pi k out randomly a ard in a 52 playing ards de k. Consider the events :• A : Pi king an a e ;• K : Pi king an king ;• D : Pi king an diamond ; • B : Pi king an bla k ard ;

• F : Pi king an gure (ja k, queenor king) ;Give the probability of the events :(a) A ;(b) K ;( ) D ;(d) B ;(e) F ;(f) A ∩D ;(g) A ∩B ;(h) B ∩ F ;(i) A ∪D ;(j) A ∪B ;

(k) B ∪ F ;(l) A ∪ F ;(m) A ∩ F ;(n) A ∩K ∩ F ;(o) A ∪K ∪ F ;(p) A ∩K ;(q) A ∪K ;

Venn diagram1. Let Ω be an universe, A and B two subsets of Ω. Illustrate with Venn diagrams thefollowing situations :(a) Ω = 1; 2; 3; 4; 5; 6;A = 1; 5; 6 and B = 2; 5.(b) Ω=blue ;white ;red ;yellow ; A =blue ;yellow and B =red.( ) Ω = a; b; c; d; e; f ; g;A = a; b; f ; g; e and B = b; c; d.2. in a lass with 25 students, 15 play musi , 8 play hess and 3 play both musi and hess.(a) Draw the Venn diagram related to the situation.(b) How many students play neither musi nor hess ?