0
votes
0answers
39 views

Generalized distributive law

Let $p,q,r,C_{ij}$ be formulae in propositional logic, or even simply symbols, i'm only interested in notations. Distributive law says: $$p\vee (q\wedge r)=(p\vee q)\wedge (p\vee r)$$ I want to ...
4
votes
1answer
190 views

“Sum” over logical and?

Given a continuous sequence of integers $(a, a+1, a+2, \dots, b)$ I want to write: $P_a \wedge P_{a+1} \wedge P_{a+2} \wedge \dots \wedge P_b$ Where $P_i$ is some logical statement parametrized by ...
4
votes
2answers
227 views

Is there notation for “some two of the three statements are true”?

There are three propositions A, B, C and another condition "some two of these propositions are true and the third one is false", or, in other words, "exactly 2 of 3 propositions are true". Using truth ...