Chapter 33 Query

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course Mth 151

3/8 Around 6:20

014. `query 14

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Question: `q3.3.5 rewrite using if then ' all marines love boot camp '.

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Your solution: if itss a marine, it loves boot camp.

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Given Solution:

`a** The statement is equivalent to 'If it's a Marine, it loves boot camp' or equivalent.

The statement is not equivalent to 'if it is boot camp, then all Marines love it', which is the converse of the original statement. **

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Question: `q3.3.18 ~p false q false p -> q true

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Your solution: false

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Given Solution:

`a** Since ~p is false then p is true.

Since q is false it follows that p -> q is of the form T ->

F, which is false.

The conditional is false when, and only when, the antecedent is true and the consequent false. **

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Question: `qQuery 3.3.36 write in symbols 'If we don't bike, then it does not rain.'

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Your solution: p->~r

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Given Solution:

`a** If p stands for 'don't bike' and r for 'it rains' then the statement would be p -> ~r. **

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Question: `qQuery 3.3.48 q true, p and r false, evaluate (-r U p) -> p

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Your solution: false

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Given Solution:

`a** The antecedent (~r U p ) would be true, since ~r true and p false.

The consequent p would be false.

Since the antecedent is true and the consequent false, the conditional is false. **

MORE DETAILED SOLUTION

r is said to be false, so ~r is true

p is said to be false

Therefore the disjunction (~r U p) would be a disjunction of a true and a false statement.

A disjunction is true if at least one of the statements is true, so (~r U p) is true.

The conditional (~r U p) -> p therefore consists of an antecedent which is true, and a consequent which is false.

By the rules for a conditional, the statement is therefore false.

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Question: `qQuery 3.3.60 truth table for (p ^ q) -> (p U q)

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Your solution:

ttttt

tfftt

ftftt

fffft

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Given Solution:

`a** The headings would be p, q ,(p^q), (pUq), (p^q)->(pUq)

Row 1 would read T T T T T

Row 2 would read T F F T T

Row 3 would read F T F T T

Row 4 would read F F F F T

The common sense of this is that whenever both p and q are true, then the statement 'p or q' must be true. That's what means to say (p ^ q) -> (p U q).

The fact that this statement is true is indicated by the last column of the truth table, which has True in every possible case. **

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