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dexar [7]
2 years ago
9

Solve.Express your answer as a simplified mixed number

Mathematics
1 answer:
weeeeeb [17]2 years ago
6 0
5/6 x 10/3 =
50/18
2 14/18
Simplified = 2 7/9
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Answer:

Step-by-step explanation:

Step 1:we should turn the “facts” into logical expressions.

Step 2:Assign variables

Our variables are: b (for butler), c (for cook), g (for gardener), h (for handyman)

Step 3 . Let the value of true indicate that the person is telling the truth. For example, b = T means the butler is telling the truth. Then we can translate the statements as follows:

Check attachment

Step 4

We know all of these must hold. So we really want to know when (b→c)∧¬(c∧g)∧¬(¬g∧¬h)∧(h → ¬c) is true.

Step 5

Behold, another truth table task! If you work out the truth table, you see that this statement is only true when:

Check attachment

Step 6

Therefore we can say the butler and cook are definitely lying, but we can not determine if the gardener or handyman are lying. However, there are four variables in this problem. Instead, we can do this with some straight reasoning. Notice that:

If the butler is telling the truth, then by (a) the cook is telling the truth.

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If the gardener is lying, then by (c) the handyman is telling the truth.

If the handyman is telling the truth, they by (d) the cook is lying.

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The answer is to G is -2
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