Let p: the book is interesting and q: the book has pictures. the notation p ∧ q represents the statement “the book is interesting the book has pictures.” the notation p ↔ q represents the statement “the book is interesting the book has pictures.” the notation q ∨ p represents the statement “the book has pictures the book is interesting.” the notation q → p represents the statement “the book is interesting the book has pictures.”

This is a Logic Problem. So we need to use operators to solve this problem. There are several operators in logic. Operators can be monadic or dyadic. A monadic operator operates on a single simple statement. Other operators will all be dyadic operators because they operate on two simple statements. 

So we have the following simple statements:

p: the book is interesting
q: the book has pictures

Thus, let's solve each notation.

First. p ∧ q

Conjunction operator. The conjunction operator creates a compound statement such that in order for the whole statement to be true, each simple statement must be true. 

Symbol: & (also ∧)
Parts of conjunction: Two simple statements joined by the conjunction symbol. 



p ∧ q: The book is interesting and the book has pictures.

Second. p ↔ q

Bi-conditional operator: The bi-conditional operator creates a compound statement such that in order for the whole statement to be true each simple statement has to have the same truth value. 

Symbol: ↔ 
Parts of bi-conditional: Two simple statements joined by the bi-conditional symbol. 



p ↔ q: The book is interesting if and only if the book has pictures.

Third. p ∨ q

Disjunction operator: The disjunction operator creates a compound statement that is true if either simple statement is true but false if both simple statements are false.

Symbol: ∨
Parts of disjunction: Two simple statements joined by the disjunction symbol



p ∨ q: The book is interesting or the book has pictures.

Fourth. p → q

Conditional operator: The conditional operator creates a compound statement that sets up a condition for something to be true. If the condition is met, the statement is true.

Symbol: →
Parts of conditional: Two simple statements joined by the conditional symbol. The first simple statement in a conditional is called the antecedent and the second simple statement is called the consequent.



p → q: If the book is interesting then the book has pictures.

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