The set E, F and G are defined as E=(odd numbers less than 13), F= ( multiples of 3 less than 15 and G=(multiples of 5 less than 20 Find E intersect G n(F union G ) (E intersect F) union G

Mathematics

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Answers

3 parts
a

E∩G={5}E \cap G = \{5\}

b

n(F∪G)=7n(F \cup G) = 7

c

(E∩F)∪G={3,5,9,10,15}(E \cap F) \cup G = \{3, 5, 9, 10, 15\}

Step-by-step solution

5 steps

Here's the breakdown of the sets and their operations:

Step 1: Define the elements of sets E, F, and G.

  • Set E: Odd numbers less than 13. E={1,3,5,7,9,11}E = \{1, 3, 5, 7, 9, 11\}
  • Set F: Multiples of 3 less than 15. F={3,6,9,12}F = \{3, 6, 9, 12\}
  • Set G: Multiples of 5 less than 20. G={5,10,15}G = \{5, 10, 15\}

Part a· 1 step

Find E intersect G

  1. Identify elements common to both E and G.

    E={1,3,5,7,9,11}E = \{1, 3, 5, 7, 9, 11\} G={5,10,15}G = \{5, 10, 15\}

    The only common element is 5.

    E∩G={5}\boxed{E \cap G = \{5\}}

Part b

n(F∪G)=7n(F \cup G) = 7

Find n(F union G)

  1. Find the union of sets F and G.

    F={3,6,9,12}F = \{3, 6, 9, 12\} G={5,10,15}G = \{5, 10, 15\}

    Combine all unique elements from F and G.

    F∪G={3,5,6,9,10,12,15}F \cup G = \{3, 5, 6, 9, 10, 12, 15\}
  2. Count the number of elements in F union G.

    There are 7 elements in F∪GF \cup G.

    n(F∪G)=7\boxed{n(F \cup G) = 7}

Part c

(E∩F)∪G={3,5,9,10,15}(E \cap F) \cup G = \{3, 5, 9, 10, 15\}

Find (E intersect F) union G

  1. Find the intersection of sets E and F.

    E={1,3,5,7,9,11}E = \{1, 3, 5, 7, 9, 11\} F={3,6,9,12}F = \{3, 6, 9, 12\}

    The common elements are 3 and 9.

    E∩F={3,9}E \cap F = \{3, 9\}
  2. Find the union of (E intersect F) and G.

    E∩F={3,9}E \cap F = \{3, 9\} G={5,10,15}G = \{5, 10, 15\}

    Combine all unique elements from {3,9}\{3, 9\} and GG.

    (E∩F)∪G={3,5,9,10,15}\boxed{(E \cap F) \cup G = \{3, 5, 9, 10, 15\}}
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