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critical thinking/logic

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use the direct and the counterexample methods to show that these arguments are invalid? For the counterexample method, display the form used.
1. There could be lightening without thunder. So, there could be thunder without lightening.

2. Nothing its better than liberty. Prison life is better than nothing. Therefore prison life us better than liberty.

3. Saying that women earn less than men because women interrupt carers to gage children, work fewer hours, obtain fewer degrees in technical areas than men, and the like of course serves the interests of successful men in the workforce who do not want their own privileges to be challenged. So, those are not the real reason for women's reduced earnings.

4. If I would make any proposition whatsoever; than by that I would have a logical error. But I do not make proposition; therefore I am not in error.

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