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Worksheet: Cartesian Products and Set Operations

Q1:

Determine ( 𝑍 βˆ’ π‘Œ ) Γ— ( 𝑋 βˆͺ π‘Œ ) using the Venn diagram below.

  • A { ( 4 , 8 ) , ( 9 , 8 ) , ( 7 , 8 ) , ( 4 , 3 ) , ( 9 , 3 ) , ( 7 , 3 ) }
  • B { ( 4 , 8 ) , ( 9 , 8 ) , ( 7 , 8 ) , ( 3 , 4 ) , ( 3 , 9 ) , ( 3 , 7 ) }
  • C { ( 8 , 4 ) , ( 8 , 9 ) , ( 8 , 7 ) , ( 4 , 3 ) , ( 9 , 3 ) , ( 7 , 3 ) }
  • D { ( 8 , 4 ) , ( 8 , 9 ) , ( 8 , 7 ) , ( 3 , 4 ) , ( 3 , 9 ) , ( 3 , 7 ) }
  • E { ( 8 , 4 ) , ( 8 , 9 ) , ( 8 , 7 ) }

Q2:

Determine ( 𝑍 βˆ’ π‘Œ ) Γ— ( 𝑋 βˆͺ π‘Œ ) using the Venn diagram below.

  • A { ( 4 , 0 ) , ( 9 , 0 ) , ( 7 , 0 ) , ( 4 , 8 ) , ( 9 , 8 ) , ( 7 , 8 ) }
  • B { ( 4 , 0 ) , ( 9 , 0 ) , ( 7 , 0 ) , ( 8 , 4 ) , ( 8 , 9 ) , ( 8 , 7 ) }
  • C { ( 0 , 4 ) , ( 0 , 9 ) , ( 0 , 7 ) , ( 4 , 8 ) , ( 9 , 8 ) , ( 7 , 8 ) }
  • D { ( 0 , 4 ) , ( 0 , 9 ) , ( 0 , 7 ) , ( 8 , 4 ) , ( 8 , 9 ) , ( 8 , 7 ) }
  • E { ( 0 , 4 ) , ( 0 , 9 ) , ( 0 , 7 ) }

Q3:

Use the Venn diagram below to find ( 𝑋 ∩ π‘Œ ) Γ— π‘Œ .

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

Q4:

Determine ( 𝑋 ) Γ— ( π‘Œ βˆͺ 𝑍 ) using the Venn diagram below.

  • A { ( 9 , 4 ) , ( 5 , 4 ) , ( 0 , 4 ) }
  • B { ( 5 , 9 ) , ( 0 , 9 ) , ( 4 , 9 ) , ( 8 , 9 ) }
  • C { ( 9 , 8 ) , ( 5 , 8 ) , ( 0 , 8 ) }
  • D { ( 9 , 5 ) , ( 9 , 0 ) , ( 9 , 4 ) , ( 9 , 8 ) }
  • E { ( 4 , 9 ) , ( 4 , 5 ) , ( 4 , 0 ) }

Q5:

Determine ( 𝑋 ) Γ— ( π‘Œ βˆͺ 𝑍 ) using the Venn diagram below.

  • A { ( 8 , 4 ) , ( 6 , 4 ) , ( 0 , 4 ) }
  • B { ( 6 , 8 ) , ( 0 , 8 ) , ( 4 , 8 ) , ( 1 , 8 ) }
  • C { ( 8 , 1 ) , ( 6 , 1 ) , ( 0 , 1 ) }
  • D { ( 8 , 6 ) , ( 8 , 0 ) , ( 8 , 4 ) , ( 8 , 1 ) }
  • E { ( 4 , 8 ) , ( 4 , 6 ) , ( 4 , 0 ) }

Q6:

Determine ( 𝑋 Γ— π‘Œ ) βˆͺ ( π‘Œ Γ— 𝑍 ) using the Venn diagram below.

  • A { ( 7 , 1 ) , ( 5 , 1 ) }
  • B { ( 7 , 5 ) , ( 7 , 0 ) , ( 7 , 2 ) , ( 5 , 5 ) , ( 5 , 0 ) , ( 5 , 2 ) }
  • C { ( 5 , 1 ) , ( 0 , 1 ) , ( 2 , 1 ) }
  • D { ( 1 , 7 ) , ( 1 , 5 ) , ( 7 , 5 ) , ( 7 , 0 ) , ( 7 , 2 ) , ( 5 , 5 ) , ( 5 , 0 ) , ( 5 , 2 ) }
  • E { ( 1 , 7 ) , ( 1 , 5 ) }

Q7:

Determine ( π‘Œ Γ— 𝑋 ) βˆͺ ( 𝑋 Γ— 𝑍 ) using the Venn diagram below.

  • A { ( 8 , 4 ) , ( 7 , 4 ) }
  • B { ( 8 , 7 ) , ( 8 , 5 ) , ( 8 , 0 ) , ( 7 , 7 ) , ( 7 , 5 ) , ( 7 , 0 ) }
  • C { ( 7 , 4 ) , ( 5 , 4 ) , ( 0 , 4 ) }
  • D { ( 8 , 4 ) , ( 7 , 4 ) , ( 4 , 7 ) , ( 4 , 5 ) , ( 4 , 0 ) }
  • E { ( 4 , 8 ) , ( 4 , 7 ) }

Q8:

Determine ( 𝑋 Γ— π‘Œ ) ∩ ( 𝑋 Γ— 𝑍 ) using the Venn diagram below.

  • A { ( 8 , 0 ) }
  • B { ( 0 , 2 ) }
  • C { ( 2 , 0 ) }
  • D { ( 0 , 8 ) }
  • E { ( 0 , 7 ) }

Q9:

Determine ( 𝑋 Γ— π‘Œ ) ∩ ( 𝑋 Γ— 𝑍 ) using the Venn diagram below.

  • A { ( 6 , 7 ) }
  • B { ( 7 , 8 ) }
  • C { ( 8 , 7 ) }
  • D { ( 7 , 6 ) }
  • E { ( 7 , 3 ) }

Q10:

Use the Venn diagram below to find 𝑋 Γ— ( π‘Œ ∩ 𝑍 ) .

  • A { ( 6 , 5 ) }
  • B { ( 5 , 1 ) }
  • C { ( 1 , 5 ) }
  • D { ( 5 , 6 ) }
  • E { ( 5 , 9 ) }

Q11:

Use the Venn diagram below to find π‘Œ Γ— ( π‘Œ ∩ 𝑍 ) .

  • A { ( 2 , 6 ) }
  • B { ( 1 , 2 ) }
  • C { ( 1 , 6 ) }
  • D { ( 2 , 6 ) , ( 6 , 6 ) }
  • E { ( 6 , 2 ) , ( 6 , 6 ) }

Q12:

Determine 𝑍 2 using the Venn diagram below.

  • A { ( 7 , 7 ) , ( 7 , 8 ) , ( 8 , 7 ) , ( 8 , 8 ) }
  • B { ( 3 , 7 ) , ( 3 , 8 ) , ( 8 , 7 ) , ( 8 , 8 ) }
  • C { ( 8 , 3 ) , ( 4 , 3 ) , ( 5 , 3 ) , ( 7 , 7 ) , ( 7 , 4 ) , ( 7 , 5 ) , ( 8 , 7 ) , ( 8 , 4 ) , ( 8 , 5 ) }
  • D { ( 8 , 8 ) , ( 8 , 4 ) , ( 8 , 5 ) , ( 4 , 8 ) , ( 4 , 5 ) , ( 4 , 4 ) , ( 5 , 8 ) , ( 5 , 4 ) , ( 5 , 5 ) }
  • E { ( 7 , 7 ) , ( 7 , 4 ) , ( 7 , 5 ) , ( 8 , 7 ) , ( 8 , 4 ) , ( 8 , 5 ) }

Q13:

Use the Venn diagram below to find ( 𝑋 Γ— 𝑍 ) βˆ’ ( 𝑋 Γ— π‘Œ ) .

  • A { ( 3 , 9 ) , ( 3 , 0 ) }
  • B { ( 4 , 3 ) , ( 7 , 3 ) }
  • C { ( 0 , 3 ) , ( 9 , 3 ) }
  • D { ( 3 , 4 ) , ( 3 , 7 ) }
  • E { ( 3 , 9 ) }

Q14:

Use the Venn diagram below to find ( 𝑋 Γ— 𝑍 ) βˆ’ ( 𝑋 Γ— π‘Œ ) .

  • A { ( 4 , 1 ) , ( 4 , 7 ) }
  • B { ( 0 , 4 ) , ( 2 , 4 ) }
  • C { ( 7 , 4 ) , ( 1 , 4 ) }
  • D { ( 4 , 0 ) , ( 4 , 2 ) }
  • E { ( 4 , 1 ) }

Q15:

Use the Venn diagram below to find ( 𝑋 Γ— π‘Œ ) βˆ’ ( 𝑋 Γ— 𝑍 ) .

  • A { ( 5 , 4 ) , ( 5 , 0 ) }
  • B { ( 7 , 5 ) , ( 2 , 5 ) }
  • C { ( 0 , 5 ) , ( 4 , 5 ) }
  • D { ( 5 , 4 ) }
  • E { ( 5 , 0 ) }

Q16:

Use the Venn diagram below to find ( 𝑋 βˆ’ π‘Œ ) Γ— π‘Œ .

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