Laws for Contradiction

1. p or c = p

Solution:
To prove `pvvc=p`, we have to first prepare the following truth table

`(1)`	`(2)`	`(3)=(1)vv(2)`
`p`	`c`	`pvvc`
T	F	T
F	F	F

from this table, we can say that columns (3) and (1) are identical.
`:. pvvc=p`

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2. p and c = c

Solution:
To prove `p^^c=c`, we have to first prepare the following truth table

`(1)`	`(2)`	`(3)=(1)^^(2)`
`p`	`c`	`p^^c`
T	F	F
F	F	F

from this table, we can say that columns (3) and (2) are identical.
`:. p^^c=c`

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3. p or not p = c

Solution:
To prove `pvv~p=c`, we have to first prepare the following truth table

`(1)`	`(2)`	`(3)=~(1)`	`(4)=(1)vv(3)`
`p`	`c`	`~p`	`pvv~p`
T	F	F	T
F	F	T	T

from this table, we can say that columns (4) and (2) are not identical.
`:. pvv~p!=c`

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