p = rain does not come
q = crops are ruined and the people will starve
p -> q
You have ~q, so ~p (contrapositive)
since q = r and s, ~r or ~s = ~q
If the rain does not come, then the crops are ruined and the people will starve. The crops are not ruined or the people will not starve.
Therefore, the rain comes.
i. Identify the premises and the conclusion.
ii. Use appropriate symbols to represent the statement in the argument.
iii. Write the argument forms using symbols.
iv. Check the validity.
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p implies q
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If the rain does not come, then the crops are ruined and the people will starve
Promise
P=q
P=q
Let's define the premise and conclusion using propositional logic:
Premise: If p, then q. (p → q)
- p: the rain does not come
- q: the crops are ruined and the people will starve
Conclusion: Either ~q or ~p. (~q V ~p)
To check the validity of the argument, we can use a truth table:
p | q | ~(p→q) | ~q | ~p | (~q V ~p)
--|---|---------|----|----|----------
T | T | F | F | F | F
T | F | T | T | F | T
F | T | F | F | T | T
F | F | F | T | T | T
Since the conclusion is true in all cases where the premise is false (rows 3 and 4), the argument is valid.
Premise: If p, then q. (p → q)
- p: the rain does not come
- q: the crops are ruined and the people will starve
Conclusion: Either ~q or ~p. (~q V ~p)
To check the validity of the argument, we can use a truth table:
p | q | ~(p→q) | ~q | ~p | (~q V ~p)
--|---|---------|----|----|----------
T | T | F | F | F | F
T | F | T | T | F | T
F | T | F | F | T | T
F | F | F | T | T | T
Since the conclusion is true in all cases where the premise is false (rows 3 and 4), the argument is valid.