Consider the following statements in respect of sets \(A\) and \(B\): I. If \(x \in A\) and \(A \in B\), then \(x \in B\). II. If \(A \subset B\) and \(x \notin B\), then \(x \notin A\). Which of the statements given above is/are correct?
II only
Statement I is false because set membership is not transitive — \(x \in A\) and \(A \in B\) do not together imply \(x \in B\). Statement II is the contrapositive of "\(A \subset B \Rightarrow (x \in A \Rightarrow x \in B)\)", which is always true, so II is correct.
Similar Questions
Consider the following statements :
1. If f is the subset of Z × Z defined by f = {(xy, x − y); x, y ∈ Z}, then f is a function from Z to Z.
2. If f is the subset of N × N defined by f = {(xy, x + y); x, y ∈ N}, then f is a function from N to N.
Which of the statements given above is/are correct?
Let S = {2, 4, 6, 8, ______ 20}.
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2. The set of all odd integers less than 100 is a finite set.
Which of the statements given above is/are correct?
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Important Questions from Set Theory and types of Sets
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If A is a subset of B and B is a subset of C, then the cardinality of A ∪ B ∪ C is equal to:
Consider the following statements :
1. If f is the subset of Z × Z defined by f = {(xy, x − y); x, y ∈ Z}, then f is a function from Z to Z.
2. If f is the subset of N × N defined by f = {(xy, x + y); x, y ∈ N}, then f is a function from N to N.
Which of the statements given above is/are correct?
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A set containing n elements, has exactly ..... subsets.
