Consider the following statements:
1. \( A = \{1, 3, 5\} \) and \( B = \{2, 4, 7\} \) are equivalent sets.
2. \( A = \{1, 5, 9\} \) and \( B = \{1, 5, 5, 9, 9\} \) are equal sets.
Which of the above statements is/are correct?
Consider the following statements:
1. The null set is a subset of every set.
2. Every set is a subset of itself.
3. If a set has 10 elements, then its power set will have 1024 elements.
Which of the above statements are correct?
Let \( R \) be a relation defined as \( xRy \) if and only if \( 2x + 3y = 20 \), where \( x, y \in \mathbb{N} \). How many elements of the form \( (x, y) \) are there in \( R \)?
Consider the following statements:
1. A function \( f: \mathbb{Z} \rightarrow \mathbb{Z} \), defined by \( f(x) = x + 1 \), is one-one as well as onto.
2. A function \( f: \mathbb{N} \rightarrow \mathbb{N} \), defined by \( f(x) = x + 1 \), is one-one but not onto.
Which of the above statements is/are correct?
Consider the following in respect of a complex number \( Z \):
1. \( \overline{(Z^{-1})} = (\bar{Z})^{-1} \)
2. \( Z\bar{Z} = |Z|^{2} \)
Which of the above is/are correct?
Consider the following statements in respect of an arbitrary complex number \( Z \):
1. The difference of \( Z \) and its conjugate is zero or a purely imaginary number.
2. The sum of \( Z \) and its conjugate is a real number.
Which of the above statements is/are correct?
