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igomit [66]
3 years ago
11

At Jack’s birthday party, 23 of the kids had balloons. 14 of the balloons were red. What fraction of the kids at the party had r

ed balloons?
Mathematics
1 answer:
Nonamiya [84]3 years ago
7 0
14/23. You can’t simplify it anymore. It is also equivalent to about 61% (60.86% to be exact)
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Answer:

The answer is \{(1,1),(2,2),(3,3),(4,4),(1,2)(2,3)(3,4),(1,3),(1,4)\}

Step-by-step explanation:

Remember that a reflexive relation R\subset \mathcal{P}(X), where \mathcal{P}(X) is the power set of X, is one which conteins the ordered pairs of the form (a,a), for a\in X.

So, As the reflexive and transitive closure of R (that we will denote by \overline{R}) is in particular reflexive, we must add to R  the elements \{(1,1) , (2,2),(3,3),(4,4) \}

A transitive relation R is one in which if the pair (a,b) and the pair (b,c) are in there, then the pair (a,c) must be there too.

So, to complete the relation R to be reflexive and transitive we must add the pair (1,3) (because (1,2),(2,3) are in R), the pair (2,4), and the pair (1,4) because we added the pair (2,4).

Therfore we have that \overline{R}=\{(1,1),(2,2),(3,3),(4,4),(1,2)(2,3)(3,4),(1,3),(1,4)\}.

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