Understanding Sets with Venn Diagrams in Junior Certificate Ordinary Level Mathematics
Dive into the world of sets and Venn diagrams with this educational content designed for Junior Certificate Ordinary Level students. Explore shading regions, identifying subsets, and solving problems using Venn diagrams to enhance your mathematical skills.
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Junior Certificate Ordinary Level Sets www.mathsplus.ie www.mathsplus.ie
(a) (i) Using the Venn diagram below, shade in the region that represents P Q. P Q P Q
(a) (ii) Using the Venn diagram below, shade in the region that represents P Q. P Q P Q
(a) (iii) Using the Venn diagram below, shade in the region that represents P \ Q. P\ Q P Q
(a) (iv) Using the Venn diagram below, shade in the region that represents (P Q) . P Q ( ) P Q
(a) A = {1, 2, 3, 4, 5} B = {2, 4, 6, 8}. ?? ?? ? ?? ?? Fill the elements of A and B into the following Venn diagram: A B 6 3 2 4 1 8 5
(c) There are 33 students in a class, 11 play hurling (H) and 23 play football (F). 4 play both sports. Using the Venn diagram below, or otherwise, answer the following questions: How many play hurling but not How many play football but not hurling? 26 (i) (ii) (iii) (iv) football? How many play neither football nor hurling? How many play exactly one of the two sports? 7 19 3 7 + 19 H F 4 11 4 7 23 4 19 3 30
(a) P = {x, y, w}. (i) element. Write down any subset of P that has one {x} or {y} or {w} (ii) elements. Write down any subset of P that has two {x, y} or {x, w} or {y, w}
A = {a, b, c, d, e} B = {c, d, f, g}. ?? ?? ? ?? ?? (a) Fill the elements of A and B into the following Venn diagram: A B f b c d a g e 4 7 # B = # A = # (A B) = 5
(c) There are 30 students in a class. 21 own a mobile phone (M) and 12 own a computer (C). 7 own both a mobile phone and a computer. Represent this information in the Venn diagram below. (i) 21 7 = 14 12 7 = 5 30 26 = 4 M C + + 14 7 5 4 26
(c) There are 30 students in a class. 21 own a mobile phone (M) and 12 own a computer (C). 7 own both a mobile phone and a computer. How many students own a mobile phone but not a computer? (ii) 14 M C 14 7 5 4
(c) There are 30 students in a class. 21 own a mobile phone (M) and 12 own a computer (C). 7 own both a mobile phone and a computer. How many students own neither a mobile phone nor a computer? (iii) 4 M C 14 7 5 4
(c) There are 30 students in a class. 21 own a mobile phone (M) and 12 own a computer (C). 7 own both a mobile phone and a computer. How many students do not own a mobile phone? (iv) 9 M C 14 7 5 4
(a) (i) Using the Venn diagram below, shade in the region that represents A B. A B A B
(a) (ii) Using the Venn diagram below, shade in the region that represents A B. A B A B
(c) In a class, all the students study Science (S) or Technical Graphics (T). A number of the students study both of these subjects. 22 students study Science. 12 students study Technical Graphics. 8 study both subjects. Represent this information in the Venn diagram below. (i) S = T = 22 8 12 8 T S 8 14 4
(c) In a class, all the students study Science (S) or Technical Graphics (T). A number of the students study both of these subjects. 22 students study Science. 12 students study Technical Graphics. 8 study both subjects. How many students study Science only? (ii) 14 T S 8 14 4
(c) In a class, all the students study Science (S) or Technical Graphics (T). A number of the students study both of these subjects. 22 students study Science. 12 students study Technical Graphics. 8 study both subjects. How many students are there in the class? (iii) 14 + 8 + 4 = 26 T S 8 14 4
(c) In a class, all the students study Science (S) or Technical Graphics (T). A number of the students study both of these subjects. 22 students study Science. 12 students study Technical Graphics. 8 study both subjects. How many students study only one of the two subjects? (iv) 14 + 4 = 18 T S 8 14 4
(a) S = {a, b, c}. (i) element. Write down a subset of S that has one {a} or {b} or {c} (ii) elements. Write down a subset of S that has two {a, b} or {a, c} or {b, c}
(a) P = {w, x, y, z} Q = {v, w, x}. ? ? ? ? ?? ? Fill the elements of P and Q into the following Venn diagram: P Q y w x v z
(c) In a survey, a group of students were asked if they were studying French or German at school. 80 of these students said they were studying French (F). 24 of these students said they were studying German (G). 15 of these students said they were studying both French and German.11 of these students said they were studying neither of the two languages. (i) Represent this information in the Venn diagram below. F G 80 15 65 24 15 9 15 11
(c) In a survey, a group of students were asked if they were studying French or German at school. 80 of these students said they were studying French (F). 24 of these students said they were studying German (G). 15 of these students said they were studying both French and German.11 of these students said they were studying neither of the two languages. How many students were in the group? How many students did not study German? 76 100 (ii) (iii) F G 65 9 15 11
(a) (i) Using the Venn diagram below, shade in the region that represents A B. A B A B
(a) (ii) Using the Venn diagram below, shade in the region that represents A \ B. A\ B A B
(c) In a survey, a group of 72 students were asked if they played basketball or tennis. 37 of these students said they played basketball (B). 30 of these students said they played tennis (T). 28 of these students said they played basketball but not tennis. (i) Represent this information in the Venn diagram below. 37 28 B T 9 28 30 9 21 72 58 14 58
(c) In a survey, a group of 72 students were asked if they played basketball or tennis. 37 of these students said they played basketball (B). 30 of these students said they played tennis (T). 28 of these students said they played basketball but not tennis. How many students played neither basketball nor tennis? 14 9 72 (ii) (iii) What percentage of the students surveyed played both basketball and tennis? __ 100 = 12 5% B T 9 28 21 14
(a) S = {w, x, y, z}. (i) element. Write down any subset of S that has one {w} or {x} or {y} or {z} (ii) elements. Write down any subset of S that has three {w, x, y}or {w, x, z} or {w, y, z} or {x, y, z}
