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From the Venn-diagram, answer the following questions: a) What is the cardinal number of the universal set? b) Write the set (G n K) by listing method. c) Prove that: G U H = G U H d) What percent of the elements of universal set U have (G U H U K)?

Mathematics

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Answer

a
9

Step-by-step solution

2 steps

Here are the solutions to the questions based on the provided Venn diagram. Question 2 cannot be answered as the tax information is missing.

Part 1

From the Venn-diagram given alongside answer the following questions.

The elements in the Venn diagram are:
Universal Set U={a,b,c,d,e,f,g,i,m}U = \{a, b, c, d, e, f, g, i, m\}
Set G={a,b,c,g,i}G = \{a, b, c, g, i\}
Set H={c,d,e,g}H = \{c, d, e, g\}
Set K={f,g,i}K = \{f, g, i\}

Part a9

What is the cardinal number of the universal set U?

  1. List all distinct elements in the universal set U from the Venn diagram.

    U={a,b,c,d,e,f,g,i,m}U = \{a, b, c, d, e, f, g, i, m\}
  2. Count the number of elements in U.

    ∣U∣=9|U| = 9

    The cardinal number of the universal set U is 9\boxed{9}.

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