Prove Commutative laws :

1. p or q = q or p

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

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

from this table, we can say that columns (3) and (4) are identical.
`:. pvvq=qvvp`

---

2. p and q = q and p

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

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

from this table, we can say that columns (3) and (4) are identical.
`:. p^^q=q^^p`

---

---

---