Given the set \(A = \{a, b, c\}\), we need to find the number of binary operations on A.
A binary operation on A is a function from \(A \times A\) to A.
The number of elements in A is |A| = 3.
The number of elements in \(A \times A\) is \(|A \times A| = |A| \times |A| = 3 \times 3 = 9\).
For each of the 9 elements in \(A \times A\), the binary operation can map it to any of the 3 elements in A.
Therefore, the total number of binary operations is \(3^{|A \times A|} = 3^9\).
Thus, the correct option is (D) \(3^9\).
For a set \( A = \{a, b, c\} \), the number of binary operations on \( A \) is calculated as follows:
1. A binary operation takes two elements from the set and maps them to one element in the set.
2. For each pair of elements from \( A \), there are 3 possible outcomes, since \( A \) has 3 elements. Since there are 3 elements in \( A \), the total number of ordered pairs of elements is \( 3 \times 3 = 9 \).
3. For each of these 9 pairs, there are 3 choices for the result.
Therefore, the total number of binary operations is: \[ 3^9 \] Answer: (D) \( 3^9 \).
The mean of coefficients of x, x2, ....., x7 in the binomial expansion of (2 + x)9 is?
The number of rational terms in the expansion of (33/4 + 53/2)60?
You are given a dipole of charge \( +q \) and \( -q \) separated by a distance \( 2l \). A sphere 'A' of radius \( R \) passes through the centre of the dipole as shown below and another sphere 'B' of radius \( 2R \) passes through the charge \( +q \). Then the electric flux through the sphere A is