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Worksheet: Properties of Cartesian Products

Q1:

If 𝑋 = { 0 , 2 , βˆ’ 1 3 , 1 4 , 1 5 } , find 𝑛 ο€Ή 𝑋  2 .

Q2:

Given that 𝑋 = { 0 , βˆ’ 1 } and π‘Œ = { 8 , βˆ’ 4 , βˆ’ 3 , βˆ’ 2 } , then which of the following relations would ( βˆ’ 1 , βˆ’ 4 ) be an element of?

  • A 𝑋 2
  • B π‘Œ Γ— 𝑋
  • C π‘Œ 2
  • D 𝑋 Γ— π‘Œ

Q3:

If 𝑋 = { 6 , 1 4 , βˆ’ 1 } and π‘Œ = { βˆ’ 8 , 9 , 5 , βˆ’ 3 } , find 𝑛 ( 𝑋 Γ— π‘Œ ) .

Q4:

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

Q5:

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

Q6:

If 𝑋 Γ— π‘Œ = { ( 8 , 0 ) , ( 8 , 6 ) , ( 1 , 0 ) , ( 1 , 6 ) , ( 3 , 0 ) , ( 3 , 6 ) } , find 𝑋 .

  • A { 8 , 6 }
  • B { 0 , 6 }
  • C { 0 , 1 , 3 }
  • D { 8 , 1 , 3 }

Q7:

If 𝑋 Γ— π‘Œ = { ( 0 , 8 ) , ( 0 , 1 ) , ( 0 , 3 ) , ( 6 , 8 ) , ( 6 , 1 ) , ( 6 , 3 ) } , find π‘Œ .

  • A { 0 , 1 , 3 }
  • B { 0 , 6 }
  • C { 8 , 6 }
  • D { 8 , 1 , 3 }

Q8:

If , which of the following points belongs to the Cartesian product of ?

  • A
  • B
  • C
  • D

Q9:

If 𝑛 ( 𝑋 ) = 1 0 0 2 , find 𝑛 ( 𝑋 ) .

Q10:

Which of the following graphs represents the set { 4 } Γ— [ 0 , 5 ] ?

  • A ( c )
  • B ( b )
  • C ( d )
  • D ( a )

Q11:

If 𝑛 ( 𝑋 ) = 1 9 and 𝑛 ( 𝑋 Γ— π‘Œ ) = 1 3 3 , find 𝑛 ( π‘Œ ) .

Q12:

If 𝑛 ( 𝑋 ) = 1 and 𝑛 ( 𝑋 Γ— π‘Œ ) = 1 0 , find 𝑛 ( π‘Œ ) .

Q13:

If ( 𝑋 βˆ’ π‘Œ ) Γ— π‘Œ = { ( βˆ’ 4 , 0 ) , ( βˆ’ 4 , 3 ) } and 𝑛 ( 𝑋 Γ— π‘Œ ) = 6 , find 𝑋 .

  • A { βˆ’ 4 }
  • B { 0 , 3 }
  • C { 3 , βˆ’ 4 }
  • D { 0 , 3 , βˆ’ 4 }
  • E { 3 , βˆ’ 4 , 6 }

Q14:

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