If `A = {a, b, c, e,f},B = {c, d, e,g} and C = {b, c,f,g}`. Then, `A - ( B cap C )` is equal to

Options

A. `{a, b, d, e}`
B. `{a, b, e, f}`
C. `phi`
D. None of these

Answer

To solve the problem, we need to find \( A - (B \cap C) \). Let's break this down step by step.

**Step 1: Identify the sets.**
- Given sets are:
- \( A = \{a, b, c, e, f\} \)
- \( B = \{c, d, e, g\} \)
- \( C = \{b, c, f, g\} \)

**Step 2: Find the intersection of sets B and C.**
- The intersection \( B \cap C \) consists of elements that are common to both sets \( B \) and \( C \).
- Elements in \( B \) are \( \{c, d, e, g\} \) and elements in \( C \) are \( \{b, c, f, g\} \).
- The common elements are:
- \( c \) (present in both sets)
- Therefore, \( B \cap C = \{c\} \).

**Step 3: Subtract the intersection from set A.**
- Now we need to perform the operation \( A - (B \cap C) \).
- We have \( A = \{a, b, c, e, f\} \) and \( B \cap C = \{c\} \).
- We will remove the element \( c \) from set \( A \):
- \( A - \{c\} = \{a, b, e, f\} \).

**Final Answer:**
- Therefore, \( A - (B \cap C) = \{a, b, e, f\} \).

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