Let $ U = \{ \text{Natural numbers from 1 to 10} \} $, $ K = \{ \text{Factors of 6} \} $, and $ L = \{ \text{Even numbers} \} $. Fill in the Venn diagram below: ![Venn Diagram](image-url) (b) Use $ \checkmark $ to indicate whether each of the following statements is true or false. Give a reason for each answer. (i) $ K \cap L = \{ \} $ (ii) $ K \neq L $ (iii) $ K \cup L = U $

Junior Cycle Mathematics Sets: Let \( U = \{ \text{Natural numb

Let $ U = \{ \text{Natural numbers from 1 to 10} \} $, $ K = \{ \text{Factors of 6} \} $, and $ L = \{ \text{Even numbers} \} $ - Junior Cycle Mathematics - Question 5 - 2013

Question 5

$Let-$-U-=-\{-\text{Natural-numbers-from-1-to-10}-\}-$,-$-K-=-\{-\text{Factors-of-6}-\}-$,-and-$-L-=-\{-\text{Even-numbers}-\}-$-Junior Cycle Mathematics-Question 5-2013.png$

Let $ U = \{ \text{Natural numbers from 1 to 10} \} $, $ K = \{ \text{Factors of 6} \} $, and $ L = \{ \text{Even numbers} \} $. Fill in the Venn diagram below... show full transcript

Worked Solution & Example Answer:Let $ U = \{ \text{Natural numbers from 1 to 10} \} $, $ K = \{ \text{Factors of 6} \} $, and $ L = \{ \text{Even numbers} \} $ - Junior Cycle Mathematics - Question 5 - 2013

Step 1

Fill in the Venn diagram below:

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Answer

In the Venn diagram, we identify the elements of the sets:

( U = { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 } )
( K = { 1, 2, 3, 6 } ) (Factors of 6)
( L = { 2, 4, 6, 8, 10 } ) (Even numbers)

The diagram would be filled as follows:

K contains {1, 2, 3, 6} (1, 2, 3 in the left circle and 6 in the overlapping section)
L contains {2, 4, 6, 8, 10} (2 and 6 in the overlap, 4, 8, and 10 in the right circle)

The completed diagram includes:

Left circle (K): 1, 3
Overlap (K ∩ L): 2, 6
Right circle (L): 4, 8, 10
Outside both circles: 5, 7, 9

Step 2

K ∩ L = { }

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Answer

False. The intersection ( K \cap L ) is ( { 2, 6 } ). Therefore, it is not empty.

Step 3

K ≠ L

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Answer

True. ( K = { 1, 2, 3, 6 } ) and ( L = { 2, 4, 6, 8, 10 } ); these sets are not equal as they contain different elements.

Step 4

K ∪ L = U

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Answer

False. The union ( K \cup L ) includes { 1, 2, 3, 4, 6, 8, 10 }. However, it does not include 5, 7, and 9, which are part of ( U ). Thus, ( K \cup L ) is not equal to ( U ).

Let \( U = \{ \text{Natural numbers from 1 to 10} \} \), \( K = \{ \text{Factors of 6} \} \), and \( L = \{ \text{Even numbers} \} \) - Junior Cycle Mathematics - Question 5 - 2013

Worked Solution & Example Answer:Let \( U = \{ \text{Natural numbers from 1 to 10} \} \), \( K = \{ \text{Factors of 6} \} \), and \( L = \{ \text{Even numbers} \} \) - Junior Cycle Mathematics - Question 5 - 2013

Fill in the Venn diagram below:

K ∩ L = { }

K ≠ L

K ∪ L = U

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