Math Problem Statement

If X = {2, 5}, Y = {1, 3, 4}, find X × Y, Y × X, X^2, and Y^2 and represent them.

Solution

It looks like you've uploaded an image that contains a set of math problems related to sets, Cartesian products, and possibly set operations. I'll interpret and help you solve the problems based on what I can see. Here are the questions I can clearly read from the image:

  1. Find the Cartesian products for sets X and Y:

    • Example: X={2,5},Y={1,3,4}X = \{2, 5\}, Y = \{1, 3, 4\}
      • Find X×YX \times Y, Y×XY \times X, X2X^2, and Y2Y^2
      • Representation using arrow diagrams
  2. Other Cartesian products and set operations:

    • X={2,5},Y={1,3,4}X = \{2, 5\}, Y = \{1, 3, 4\}
      • X×XX \times X
      • Represent using arrow diagrams
  3. Perform various operations with different sets:

    • If X={1,2},Y={3,4},Z={4,5}X = \{1, 2\}, Y = \{3, 4\}, Z = \{4, 5\}
      • Find:
        a) XYX \cup Y
        b) XYX - Y
        c) (XZ)(X \cup Z)
        d) (XZ)(X \cap Z)
  4. Set membership operations:

    • If X={2,1},Y={4,0},Z={6,3}X = \{2, -1\}, Y = \{4, 0\}, Z = \{6, 3\}
      • Find:
        a) XYX \cup Y
        b) Y×ZY \times Z
        c) XZX \cap Z
  5. Cardinality and set notation:

    • Find the number of elements in certain sets:
      a) n(XZ)n(X \cup Z)

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Math Problem Analysis

Mathematical Concepts

Sets
Cartesian Product
Set Operations

Formulas

X × Y = {(x, y) | x ∈ X and y ∈ Y}
Y × X = {(y, x) | y ∈ Y and x ∈ X}
X^2 = X × X
Y^2 = Y × Y

Theorems

Cartesian Product Definition
Set Theory

Suitable Grade Level

Grades 7-10