Question

if \\(a = \\{a, b, c, d, e, f, g\\}\\) and \\(c = \\{d, e, g, h, i, j\\}\\), find \\(c - a\\)

a
b
c
d
e
f
g
h
i

Explanation:

🆕 New Concept Discovered: Set Difference
Elements in one set but not the other

Step 1: Identify the elements of each set

We are given two sets:

$$ A = \{a, b, c, d, e, f, g\} $$

$$ C = \{d, e, g, h, i, j\} $$

Step 2: Apply the definition of set difference

The set difference \( C - A \) (also written as \( C \setminus A \)) represents the set of all elements that belong to set \( C \) but do not belong to set \( A \).

To find this, we start with the elements of \( C \) and remove any elements that are also found in \( A \):

• \( d \) is in \( A \) (remove)
• \( e \) is in \( A \) (remove)
• \( g \) is in \( A \) (remove)
• \( h \) is not in \( A \) (keep)
• \( i \) is not in \( A \) (keep)
• \( j \) is not in \( A \) (keep)

Step 3: Write the resulting set

Subtracting the common elements \( \{d, e, g\} \) from \( C \):

$$ C - A = \{h, i, j\} $$

Answer:

$$ \{h, i, j\} $$