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Please give me discrete mathematics
1

(p→q)→(q→r)

(p→q)∨(q→r) becomes conjunctive disjunction.

(? p∨q)∨(? Q∨r) becomes conjunctive disjunction.

(p∧? q)∨(? De Morgan's law

(p∧? q)∨? Q∞r associative law

Q∨r conjunctive disjunctive absorption rate

(? p∧p)∨? Q∨r complement

(? p∨? q∨r)∧(p∨? Q∨r) distribution law 2

Get the master conjunctive normal form, and then check the missing largest item.

m? ∧M∏(2,6)

∏(0, 1,3,4,5,7)? ∑(0, 1,3,4,5,7)? m? ∨m? ∨m? ∨m? ∨m? ∨m?

(p∨q∨r)∨? (p∨q∨? r)∨? (p∨? q∨? r)∨? (? p∨q∨r)∨? (? p∨q∨? r)∨? (? p∨? q∨? De Morgan's law

(? p∧? q∧? r)∩(? p∧? q∧r)∨(? p∧q∧r)∨(p∧? q∧? r)∩(p∧? Q∧r)∨(p∧q∧r) De Morgan's Law

Get the principal disjunctive normal form

2

P(A)={? ,{ 1},{2},{ 1,2}}

P(A)×A={(? , 1),({ 1}, 1}), ({2}, 1), ({ 1,2}, 1), (? ,2),({ 1},2}), ({2},2), ({ 1,2},2)}

three

R = { & ltb,a & gt,& ltb,c & gt,& ltc,a & gt,& ltc,d & gt,& ltd,b & gt}

Reflexive closure r (r) =

1 0 0 0

1 1 1 0

1 0 1 1

0 1 0 1

Symmetric closure s (r) =

0 1 1 0

1 0 1 1

1 1 0 1

0 1 1 0

Transitive closure t (r) =

0 0 0 0

1 1 1 1

1 1 0 1

1 1 1 1

four

Hastu

Turn left | turn right

Set b = {4,6}

The largest element is 4,6.

The smallest element is 4, 6.

Infinite certainty

There is a lower bound of 2.