Prove Absorption laws

1. p and (p or q) = p

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

`(1)`	`(2)`	`(3)=(1)vv(2)`	`(4)=(1)^^(3)`
`p`	`q`	`pvvq`	`p^^(pvvq)`
T	T	T	T
T	F	T	T
F	T	T	F
F	F	F	F

from this table, we can say that columns (4) and (1) are identical.
`:. p^^(pvvq)=p`

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2. p or (p and q) = p

Solution:
To prove `pvv(p^^q)=p`, we have to first prepare the following truth table

`(1)`	`(2)`	`(3)=(1)^^(2)`	`(4)=(1)vv(3)`
`p`	`q`	`p^^q`	`pvv(p^^q)`
T	T	T	T
T	F	F	T
F	T	F	F
F	F	F	F

from this table, we can say that columns (4) and (1) are identical.
`:. pvv(p^^q)=p`

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