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If cardinality of (A U B) = cardinality of A+ cardinality of B. This means ____________a.A and B are disjointb.B is a subset of Ac.A is a subset of Bd.None of the mentioned

Question

If cardinality of (A U B) = cardinality of A+ cardinality of B. This means ____________a.A and B are disjointb.B is a subset of Ac.A is a subset of Bd.None of the mentioned

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Solution

The statement "If cardinality of (A U B) = cardinality of A+ cardinality of B" means that A and B are disjoint. This is because the cardinality of the union of two sets A and B is equal to the sum of the cardinalities of A and B if and only if A and B have no elements in common, i.e., they are disjoint. Therefore, the correct answer is a. A and B are disjoint.

Similar Questions

If cardinality of (A U B) = cardinality of A+ cardinality of B. This means ____________ a. B is a subset of A b. None of the mentioned c. A is a subset of B d. A and B are disjoint

Consider the sets:U = {1, 2, {1}, {2}, {1, 2}}     A = {1, 2, {1}}      B = {{1}, {1, 2}}     C = {2, {1}, {2}}A – B is the set:a.{1, 2}b.{1, {1, 2}}c.{ }d.{{1, 2}}

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U = {1, 2, {1}, {2}, {1, 2}}      A = {1, 2, {1}}       B = {{1}, {1, 2}}     C = {2, {1}, {2}}.Which one of the following statements is valid if x ∉ B U C? (Hint: Determine U – (B U C).)a.x ∈ {1}.b.x ∈ ⊘.c.x ∈ {1, 2}.d.x ∈ B and x ∈ C.

Consider the sets:U = {1, 2, {1}, {2}, {1, 2}}     A = {1, 2, {1}}      B = {{1}, {1, 2}}     C = {2, {1}, {2}}Ƥ (A) is the set:a.{⊘, {1}, {2}, {1, 2}, {1, 2, {1}}}b.{⊘, {1}, {2}, {{1}}, {1, 2}, {1, {1}}, {2, {1}}, {1, 2, {1}}}c.{⊘, {1}, {2}, {{1, 2}}, {1, {1}}, {2, {1}}, {1, 2, {1, 2}}}d.{⊘, {1}, {2}, {{1}}, {1, {1}}, {2, {1}}, {1, 2, {1}}}

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