Verify the first Absorption Law by means of a truth table. I know that 0 = false and 1 = true, but I'm having trouble figuring out how to write a truth table for this.

The first Absorption Law is:

p v (p ^ q) = p

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Here is what I gathered from examples in my book:

I think the table will have 4 rows. On row 1, 'P' and 'Q' will both be true; on row 2, 'P' will be true and 'Q' will be false; on row 3, 'P' will be false and 'Q' will be true; and on row 4, 'P' and 'Q' will both be false.

'P v (P & Q)' is true if either 'P' is true or 'P & Q' is true, so 'P v (P & Q)' is true whenever 'P' is true. Thus, 'P' and 'P v (P & Q)' are both true on lines 1 and 2.

'P v (P & Q)' is false if 'P' and 'P & Q' are both false. Now, 'P & Q' is false if 'P' is false, so 'P v (P & Q)' is false whenever 'P' is false. Thus, 'P' and 'P v (P & Q)' are both false on lines 3 and 4.

Thus, on each line of the truth table, the truth value that 'P' has on that line is the same as the truth value that 'P v (P & Q)' has on that line. Hence, 'P' and 'P v (P & Q)' are logically equivalent: they are true under exactly the same conditions.

How would you write this in a truth table?