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Worksheet: Different Forms of Representing Cartesian Products of Sets

Q1:

Suppose that 𝑋 βŠ‚ π‘Œ , 𝑛 ( 𝑋 Γ— π‘Œ ) = 6 , 3 ∈ 𝑋 , and ( 5 , 7 ) ∈ 𝑋 Γ— π‘Œ . Find 𝑋 .

  • A { 3 }
  • B { 3 , 7 }
  • C { 5 }
  • D { 3 , 5 }
  • E { 3 , 5 , 7 }

Q2:

𝑋 βŠ‚ π‘Œ . 𝑛 ( 𝑋 Γ— π‘Œ ) = 6 . 8 ∈ 𝑋 . ( 7 , 4 ) ∈ 𝑋 Γ— π‘Œ . Find 𝑋 Γ— π‘Œ .

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

Q3:

If 𝑋 = { 3 7 , 1 8 , 3 9 } and π‘Œ = { 9 , 1 2 } , is ( π‘Œ Γ— π‘Œ ) βŠ‚ ( 𝑋 Γ— 𝑋 ) ?

  • Ano
  • Byes

Q4:

Using the Cartesian diagram below, determine the relation 𝑋 Γ— π‘Œ .

  • A { ( 5 , 6 ) , ( 1 0 , 1 2 ) , ( 1 5 , 9 ) }
  • B { ( 6 , 5 ) , ( 9 , 1 0 ) , ( 1 2 , 1 5 ) }
  • C { ( 5 , 6 ) , ( 1 0 , 9 ) , ( 1 2 , 1 5 ) }
  • D { ( 5 , 6 ) , ( 1 0 , 9 ) , ( 1 5 , 1 2 ) }

Q5:

Using the Cartesian diagram below, determine the relation 𝑋 Γ— π‘Œ .

  • A { ( 3 , 4 ) , ( 6 , 1 2 ) , ( 9 , 8 ) }
  • B { ( 4 , 3 ) , ( 8 , 6 ) , ( 1 2 , 9 ) }
  • C { ( 3 , 4 ) , ( 6 , 8 ) , ( 1 2 , 9 ) }
  • D { ( 3 , 4 ) , ( 6 , 8 ) , ( 9 , 1 2 ) }

Q6:

Using the Cartesian diagram below, determine the relation 𝑋 Γ— π‘Œ .

  • A { ( 5 , 2 ) , ( 1 0 , 6 ) , ( 1 5 , 4 ) }
  • B { ( 2 , 5 ) , ( 4 , 1 0 ) , ( 6 , 1 5 ) }
  • C { ( 5 , 2 ) , ( 1 0 , 4 ) , ( 6 , 1 5 ) }
  • D { ( 5 , 2 ) , ( 1 0 , 4 ) , ( 1 5 , 6 ) }

Q7:

Use the arrow diagram below to find 𝑋 Γ— π‘Œ .

  • A { ( 3 , 4 ) , ( 3 , 0 ) , ( 3 , 9 ) , ( 4 , 8 ) , ( 0 , 8 ) , ( 9 , 8 ) }
  • B { ( 4 , 3 ) , ( 0 , 3 ) , ( 9 , 3 ) , ( 4 , 8 ) , ( 0 , 8 ) , ( 9 , 8 ) }
  • C { ( 9 , 4 ) , ( 9 , 0 ) , ( 3 , 4 ) , ( 3 , 0 ) , ( 8 , 4 ) , ( 8 , 0 ) }
  • D { ( 4 , 9 ) , ( 4 , 3 ) , ( 4 , 8 ) , ( 0 , 9 ) , ( 0 , 3 ) , ( 0 , 8 ) }

Q8:

Use the arrow diagram below to find 𝑋 Γ— π‘Œ .

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

Q9:

Use the arrow diagram below to find 𝑋 Γ— π‘Œ .

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