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Class XI - MATHEMATICS
Chapter – SETS
Page 2


Class XI - MATHEMATICS
Chapter – SETS
Learning Outcome
In this module we are going to learn about
• Intervals as subset of R
• Power set
• Universal set
• Venn diagrams
• Union of sets
• Intersection of sets
• Practical problems on Union & Intersection of sets
Page 3


Class XI - MATHEMATICS
Chapter – SETS
Learning Outcome
In this module we are going to learn about
• Intervals as subset of R
• Power set
• Universal set
• Venn diagrams
• Union of sets
• Intersection of sets
• Practical problems on Union & Intersection of sets
INTERV ALS AS SUBSET OF REAL NUMBERS
Open Interval: Let a, b ? R and a < b. Then the set of real 
numbers { x : a < x < b} is called an open interval and is 
denoted by (a, b).
Closed Interval: Let a, b ? R and a < b. Then the set of real 
numbers {x : a = x = b} is called closed interval and is 
denoted by [ a, b ]. 
Page 4


Class XI - MATHEMATICS
Chapter – SETS
Learning Outcome
In this module we are going to learn about
• Intervals as subset of R
• Power set
• Universal set
• Venn diagrams
• Union of sets
• Intersection of sets
• Practical problems on Union & Intersection of sets
INTERV ALS AS SUBSET OF REAL NUMBERS
Open Interval: Let a, b ? R and a < b. Then the set of real 
numbers { x : a < x < b} is called an open interval and is 
denoted by (a, b).
Closed Interval: Let a, b ? R and a < b. Then the set of real 
numbers {x : a = x = b} is called closed interval and is 
denoted by [ a, b ]. 
TYPES OF INTERV ALS
? (a, b)     = { x : a < x < b, x ? R} 
? [a, b]     = {x : a = x = b, x ? R}
? (a, b]     = { x : a < x = b, x ? R} 
? [a, b)     = { x : a = x < b, x ? R} 
? (0, 8) = { x : 0 < x < 8, x ? R}
? (- 8,8)  = {x: -8 < x < 8, x ? R} = the set of real numbers R. 
Page 5


Class XI - MATHEMATICS
Chapter – SETS
Learning Outcome
In this module we are going to learn about
• Intervals as subset of R
• Power set
• Universal set
• Venn diagrams
• Union of sets
• Intersection of sets
• Practical problems on Union & Intersection of sets
INTERV ALS AS SUBSET OF REAL NUMBERS
Open Interval: Let a, b ? R and a < b. Then the set of real 
numbers { x : a < x < b} is called an open interval and is 
denoted by (a, b).
Closed Interval: Let a, b ? R and a < b. Then the set of real 
numbers {x : a = x = b} is called closed interval and is 
denoted by [ a, b ]. 
TYPES OF INTERV ALS
? (a, b)     = { x : a < x < b, x ? R} 
? [a, b]     = {x : a = x = b, x ? R}
? (a, b]     = { x : a < x = b, x ? R} 
? [a, b)     = { x : a = x < b, x ? R} 
? (0, 8) = { x : 0 < x < 8, x ? R}
? (- 8,8)  = {x: -8 < x < 8, x ? R} = the set of real numbers R. 
REPRESENTING INTERV ALS ON 
NUMBER LINE
(a, b)
[a, b]
(a, b]
[a, b)
a                            b
a                                      b
a                                    b
a b
?
?
?
?