Laws for Tautology

1. p or t = t

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

`(1)`	`(2)`	`(3)=(1)vv(2)`
`p`	`t`	`pvvt`
T	T	T
F	T	T

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

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2. p and t = t

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

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

from this table, we can say that columns (3) and (2) are not identical.
`:. p^^t!=t`

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3. p or not p = t

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

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

from this table, we can say that columns (4) and (2) are identical.
`:. pvv~p=t`

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