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Lesson: Cartesian Products and Set Operations

Sample Question Videos

Worksheet • 25 Questions • 3 Videos

Q1:

If 𝑋 = { 2 , 6 , 7 } , find 𝑋 2 .

  • A { ( 2 , 2 ) , ( 2 , 6 ) , ( 2 , 7 ) , ( 6 , 2 ) , ( 6 , 6 ) , ( 6 , 7 ) , ( 7 , 2 ) , ( 7 , 6 ) , ( 7 , 7 ) }
  • B { ( 2 , 2 ) , ( 2 , 6 ) , ( 2 , 7 ) , ( 6 , 2 ) , ( 6 , 7 ) , ( 7 , 7 ) , ( 7 , 2 ) , ( 2 , 7 ) , ( 2 , 2 ) }
  • C { ( 2 , 2 ) , ( 2 , 6 ) , ( 2 , 7 ) , ( 2 , 2 ) , ( 6 , 6 ) , ( 6 , 7 ) , ( 7 , 2 ) , ( 7 , 6 ) }
  • D { ( 2 , 2 ) , ( 2 , 6 ) , ( 2 , 7 ) , ( 6 , 2 ) , ( 6 , 7 ) , ( 7 , 7 ) , ( 7 , 2 ) , ( 7 , 6 ) }

Q2:

If 𝑋 = { 2 , 3 } , find 𝑋 Γ— βˆ… .

  • A βˆ…
  • B { ( 2 , 3 ) , ( 3 , 2 ) }
  • C { ( 3 , 2 ) }
  • D { ( 2 , 3 ) }

Q3:

If 𝑋 = { 8 } , π‘Œ = { 8 , 3 } , and 𝑍 = { 9 , 4 , 5 } , find ( 𝑋 Γ— π‘Œ ) βˆͺ ( π‘Œ Γ— 𝑍 ) .

  • A { ( 3 , 5 ) , ( 8 , 3 ) , ( 8 , 9 ) , ( 8 , 8 ) , ( 3 , 9 ) , ( 8 , 5 ) , ( 3 , 4 ) , ( 8 , 4 ) }
  • B { ( 8 , 3 ) , ( 8 , 8 ) , ( 3 , 9 ) , ( 3 , 4 ) , ( 3 , 5 ) }
  • C { ( 4 , 8 ) , ( 9 , 8 ) , ( 9 , 3 ) , ( 3 , 8 ) , ( 8 , 8 ) , ( 4 , 3 ) , ( 5 , 8 ) , ( 5 , 3 ) }
  • D { ( 8 , 3 ) , ( 4 , 8 ) , ( 9 , 8 ) , ( 9 , 3 ) , ( 8 , 8 ) , ( 4 , 3 ) , ( 5 , 8 ) , ( 5 , 3 ) }
  • E { ( 3 , 5 ) , ( 3 , 8 ) , ( 8 , 9 ) , ( 8 , 8 ) , ( 3 , 9 ) , ( 8 , 5 ) , ( 3 , 4 ) , ( 8 , 4 ) }

Q4:

If 𝑋 = { 9 , 3 , 7 } and π‘Œ = { 3 , 4 } , find ( 𝑋 Γ— π‘Œ ) ∩ π‘Œ 2 .

  • A { ( 3 , 4 ) , ( 3 , 3 ) }
  • B { ( 3 , 3 ) , ( 4 , 3 ) }
  • C { ( 3 , 7 ) , ( 3 , 9 ) , ( 3 , 3 ) }
  • D { ( 7 , 3 ) , ( 9 , 3 ) , ( 3 , 3 ) }

Q5:

If 𝑋 Γ— π‘Œ = { ( 8 , 9 ) , ( 8 , 1 ) , ( 8 , 3 ) } , find π‘Œ Γ— 𝑋 .

  • A { ( 9 , 8 ) , ( 1 , 8 ) , ( 3 , 8 ) }
  • B { ( 8 , 8 ) }
  • C { ( 8 , 9 ) , ( 1 , 9 ) , ( 3 , 9 ) }
  • D { ( 9 , 9 ) , ( 9 , 1 ) , ( 9 , 3 ) , ( 1 , 9 ) , ( 1 , 1 ) , ( 1 , 3 ) , ( 3 , 9 ) , ( 3 , 1 ) , ( 3 , 3 ) }

Q6:

If 𝑋 = { 2 , 3 } , π‘Œ = { 5 , 7 } , and 𝑍 = { 7 } , find ( 𝑋 Γ— π‘Œ ) ∩ ( 𝑋 Γ— 𝑍 ) .

  • A { ( 2 , 7 ) , ( 3 , 7 ) }
  • B βˆ…
  • C { ( 7 , 3 ) , ( 7 , 2 ) }
  • D { ( 2 , 7 ) , ( 3 , 7 ) , ( 2 , 5 ) , ( 3 , 5 ) }

Q7:

If 𝑋 = { 4 } , π‘Œ = { 8 , 1 , 6 } , and 𝑍 = { 8 , 4 } , find ( 𝑋 Γ— π‘Œ ) ∩ ( 𝑋 Γ— 𝑍 ) .

  • A { ( 4 , 8 ) }
  • B βˆ…
  • C { ( 8 , 4 ) }
  • D { ( 4 , 1 ) , ( 4 , 6 ) , ( 4 , 8 ) }

Q8:

If 𝑋 βˆ’ π‘Œ = { 8 , 3 , 6 } , π‘Œ βˆ’ 𝑋 = { 4 } , and 𝑋 ∩ π‘Œ = { 2 } , find ( 𝑋 Γ— π‘Œ ) ∩ ( π‘Œ Γ— 𝑋 ) .

  • A { ( 2 , 2 ) }
  • B { ( 8 , 4 ) , ( 3 , 4 ) , ( 6 , 4 ) }
  • C { ( 4 , 8 ) , ( 4 , 3 ) , ( 4 , 6 ) }
  • D { ( 8 , 2 ) , ( 3 , 2 ) , ( 6 , 2 ) }

Q9:

If { 3 1 } Γ— { π‘₯ , 𝑦 } = { ( 3 1 , 2 5 ) , ( 3 1 , 4 6 ) } , find all the possible values of π‘₯ + 𝑦 .

  • A71
  • B77
  • C βˆ’ 2 1
  • D56
  • E21

Q10:

If π‘Œ = { 4 2 , 2 2 } and 𝑋 = { 7 , 4 2 } , which of the following is equal to 𝑋 Γ— ( 𝑋 ∩ π‘Œ ) ?

  • A ( 𝑋 Γ— 𝑋 ) ∩ ( 𝑋 Γ— π‘Œ )
  • B ( 𝑋 Γ— 𝑋 ) βˆͺ ( 𝑋 Γ— π‘Œ )
  • C π‘Œ Γ— ( 𝑋 ∩ π‘Œ )
  • D ( 𝑋 Γ— 𝑋 ) βˆ’ ( 𝑋 Γ— π‘Œ )

Q11:

If π‘Œ = { 3 3 , 4 6 } and 𝑋 = { 4 4 , 3 3 } , which of the following is equal to π‘Œ Γ— ( 𝑋 βˆͺ π‘Œ ) ?

  • A ( π‘Œ Γ— 𝑋 ) βˆͺ ( π‘Œ Γ— π‘Œ )
  • B ( π‘Œ Γ— 𝑋 ) ∩ ( π‘Œ Γ— π‘Œ )
  • C π‘Œ Γ— ( 𝑋 ∩ π‘Œ )
  • D ( π‘Œ Γ— 𝑋 ) βˆ’ ( π‘Œ Γ— π‘Œ )

Q12:

Which of the following Cartesian products would give the result { ( 2 0 , 3 7 ) , ( 2 0 , 1 1 ) } ?

  • A { 2 0 } Γ— { 3 7 , 1 1 }
  • B { 3 7 , 1 1 } Γ— { 2 0 }
  • C { 2 0 } Γ— { 1 1 }
  • D { 2 0 } Γ— { 3 7 }

Q13:

If 𝑋 Γ— π‘Œ = { ( 2 , 9 ) , ( 2 , 6 ) , ( 7 , 9 ) , ( 7 , 6 ) } , find π‘Œ 2 .

  • A { ( 9 , 9 ) , ( 9 , 6 ) , ( 6 , 9 ) , ( 6 , 6 ) }
  • B { ( 2 , 2 ) , ( 2 , 7 ) , ( 7 , 2 ) , ( 7 , 7 ) }
  • C { ( 2 , 2 ) , ( 2 , 6 ) , ( 6 , 2 ) , ( 6 , 6 ) }
  • D { ( 9 , 9 ) , ( 9 , 7 ) , ( 7 , 9 ) , ( 7 , 7 ) }

Q14:

If 𝑋 Γ— π‘Œ = { ( 9 , 8 ) , ( 9 , 2 ) , ( 2 , 8 ) , ( 2 , 2 ) , ( 6 , 8 ) , ( 6 , 2 ) } , find 𝑛 ( 𝑋 ) .

Q15:

If 𝑋 βŠ‚ π‘Œ and 𝑋 Γ— π‘Œ = { ( π‘Ž , 3 ) , ( π‘Ž , 2 ) , ( π‘Ž , 9 ) , ( 2 , 3 ) , ( 2 , 2 ) , ( 2 , 9 ) } , find all the possible values of π‘Ž .

  • A3 or 9
  • B3 or 2
  • C2
  • D2 or 9

Q16:

If 𝑋 = { ( 5 , 5 ) , ( 5 , 2 ) , ( 5 , 1 9 ) , ( 2 , 5 ) , ( 2 , 2 ) , ( 2 , 1 9 ) , ( 1 9 , 5 ) , ( 1 9 , 2 ) , ( 1 9 , 1 9 ) } 2 , find 𝑋 .

  • A { 5 , 2 , 1 9 }
  • B { 5 , 2 }
  • C { 5 , 1 9 }
  • D { 1 9 , 2 }

Q17:

If 𝑋 = { 1 } , π‘Œ = { 3 , 4 } , and 𝑍 = { 2 , 5 } , find ( 𝑍 βˆ’ π‘Œ ) Γ— ( 𝑋 βˆͺ π‘Œ ) .

  • A { ( 2 , 1 ) , ( 2 , 3 ) , ( 2 , 4 ) , ( 5 , 1 ) , ( 5 , 3 ) , ( 5 , 4 ) }
  • B { ( 2 , 1 ) , ( 3 , 1 ) , ( 4 , 1 ) , ( 5 , 1 ) }
  • C { ( 3 , 1 ) , ( 3 , 3 ) , ( 3 , 4 ) , ( 4 , 1 ) , ( 4 , 3 ) , ( 4 , 4 ) }
  • D { ( 2 , 3 ) , ( 2 , 4 ) , ( 5 , 3 ) , ( 5 , 4 ) }
  • E { ( 1 , 2 ) , ( 1 , 5 ) , ( 3 , 2 ) , ( 3 , 5 ) , ( 4 , 2 ) , ( 4 , 5 ) }

Q18:

For two sets 𝑋 and π‘Œ , a function 𝑓 exists from 𝑋 to π‘Œ . Also, π‘Ž ∈ 𝑋 , 𝑏 ∈ π‘Œ , and π‘Ž 𝑅 𝑏 means 𝑏 is divisible by π‘Ž . If 𝑋 βˆͺ π‘Œ = { 2 , 4 , 7 , 9 , 1 3 , 1 6 , 2 1 } , 𝑛 ( 𝑋 ) = 3 , and 𝑛 ( 𝑋 Γ— π‘Œ ) = 1 2 , determine 𝑅 .

  • A 𝑅 = { ( 2 , 1 6 ) , ( 4 , 1 6 ) , ( 7 , 2 1 ) }
  • B 𝑅 = { ( 2 , 1 6 ) , ( 4 , 1 6 ) , ( 7 , 2 1 ) , ( 2 , 9 ) }
  • C 𝑅 = { ( 1 6 , 2 ) , ( 1 6 , 4 ) , ( 2 1 , 7 ) }
  • D 𝑅 = { ( 2 , 9 ) , ( 4 , 1 3 ) , ( 7 , 1 6 ) }
  • E 𝑅 = { ( 2 , 1 6 ) , ( 4 , 1 6 ) , ( 7 , 9 ) }

Q19:

If 𝑋 = { 9 , 5 } , π‘Œ = { 3 , 4 } , and 𝑍 = { 4 } , find ( 𝑋 βˆ’ π‘Œ ) Γ— 𝑍 .

  • A { ( 9 , 4 ) , ( 5 , 4 ) }
  • B { ( 3 , 4 ) , ( 4 , 4 ) }
  • C { ( 4 , 3 ) , ( 4 , 4 ) }
  • D { ( 4 , 9 ) , ( 4 , 5 ) }

Q20:

If 𝑋 = { 2 } , π‘Œ = { 4 } , and 𝑍 = { 2 , 7 } , find ( 𝑋 βˆ’ π‘Œ ) Γ— ( π‘Œ βˆ’ 𝑍 ) .

  • A { ( 2 , 4 ) }
  • B { ( 2 , 2 ) , ( 7 , 2 ) }
  • C { ( 4 , 2 ) }
  • D { ( 2 , 2 ) , ( 2 , 7 ) }
  • E { ( 4 , 4 ) }

Q21:

If 𝑛 ( 𝑋 ) = 2 and 𝑛 ( π‘Œ ) = 1 3 , find 𝑛 ( 𝑋 Γ— π‘Œ ) .

Q22:

If 𝑋 = { 8 , 2 } , π‘Œ = { 1 , 9 , 4 , 6 } , and 𝑍 = { 4 , 5 } , find ( 𝑋 βˆ’ π‘Œ ) Γ— ( 𝑍 ∩ π‘Œ ) .

  • A { ( 8 , 4 ) , ( 2 , 4 ) }
  • B { ( 8 , 1 ) , ( 8 , 4 ) , ( 8 , 5 ) , ( 8 , 6 ) , ( 8 , 9 ) , ( 2 , 1 ) , ( 2 , 4 ) , ( 2 , 5 ) , ( 2 , 6 ) , ( 2 , 9 ) }
  • C { ( 8 , 5 ) , ( 2 , 5 ) }
  • D { ( 1 , 4 ) , ( 9 , 4 ) , ( 4 , 4 ) , ( 6 , 4 ) }

Q23:

If 𝑋 = { 3 , 5 , 7 } , π‘Œ = { 9 , 4 , 6 , 7 } , and 𝑍 = { 9 , 4 } , find 𝑛 ( 𝑋 Γ— ( π‘Œ βˆͺ 𝑍 ) ) .

Q24:

If 𝑋 = { 9 } and π‘Œ = { 2 , 6 } , find 𝑋 Γ— π‘Œ .

  • A { ( 9 , 2 ) , ( 9 , 6 ) }
  • B { ( 2 , 9 ) , ( 6 , 9 ) }
  • C { ( 2 , 9 ) , ( 2 , 6 ) }
  • D { ( 6 , 9 ) , ( 6 , βˆ’ 3 ) }
  • E { ( 9 , 2 ) , ( 6 , 2 ) }

Q25:

If 𝑋 βŠ‚ π‘Œ , 𝑛 ( 𝑋 Γ— π‘Œ ) = 6 , ( 4 , 7 ) ∈ 𝑋 Γ— π‘Œ , and 5 ∈ 𝑋 , then find π‘Œ .

  • A { 5 , 4 , 7 }
  • B { 5 , 4 }
  • C { 6 , 5 , 7 }
  • D { 4 }
  • E { 5 , 4 , 6 }
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