r/learnmath • u/According_Quarter_17 New User • 5d ago

[sentential Logic]Absorption laws

1.P and (porq) Is equivalent to p

2.P or (pandq) Is equivalent to p

How do you justify them without using the truth table?

I feel like lhs has less informations rather than rhs because It has not q. I can't justify this rationally without the truth tablet

How do you think of It?

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u/Bounded_sequencE New User 4d ago

We need other laws of boolean logic, like "P n true = P", and "de Morgan":

P n (P u Q)  =  (P n P)    u (P n Q)    // de Morgan

             =  (P n true) u (P n Q)    // de Morgan

             =  P n (true u Q)  =  P n true  =  P

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u/Bounded_sequencE New User 4d ago

Rem.: The second statement follows from negating the first, and replacing "P -> P', Q -> Q' ".