Does the 3SAT problems have to have consistent operators?

What are the rules pertaining to 3SAT as to the actual boolean equation?

The main thing I do not understand is in a given boolean expression within a single clause can you have both AND + OR operators i.e. (x1 & x2 | x3) or do they have to remain consistent i.e. (x1 & x2 & x3) or (x1 | x2 | x3)?

That being said when connecting clauses together do the boolean operators have to be consistent?

i.e. (x1 & x2 & x3) & (x1 & x2 & x3) & (x1 & x2 & x3)

or


i.e. (x1 & x2 & x3) | (x1 & x2 & x3) | (x1 & x2 & x3)

or can they be mixed up like

i.e. (x1 & x2 & x3) | (x1 & x2 & x3) & (x1 & x2 & x3)

or


i.e. (x1 & x2 & x3) & (x1 & x2 & x3) | (x1 & x2 & x3)

Can a 3SAT problem just be a huge jumble of different logic operators or do they have to remain consistent throughout the equation? Ever example I have seen has consistent operators and I cant seem to find the answer to the question anywhere.

• 3SAT is given in 3-CNF form, look what it does mean. Curcuit SAT has no such restrictions. – rus9384 Nov 16 '17 at 1:27
• – D.W. Nov 16 '17 at 6:55
• @rus9384 Write an answer? – Yuval Filmus Nov 16 '17 at 19:22

2. Only $\lor$ operators can be used inside clauses (not counting varible negations).
3. Only $\land$ operators can be used outside clauses.