Let's carefully analyze the two chemical reactions mentioned:
### Reaction A:
[tex]\[ Ca(OH)_2 \rightarrow CaO + H_2O \][/tex]
In this reaction, calcium hydroxide ([tex]\(Ca(OH)_2\)[/tex]) breaks down into calcium oxide ([tex]\(CaO\)[/tex]) and water ([tex]\(H_2O\)[/tex]). This type of reaction, where a compound breaks down into two or more simpler substances, is known as a decomposition reaction.
### Reaction B:
[tex]\[ 4K + O_2 \rightarrow 2K_2O \][/tex]
In this reaction, potassium ([tex]\(K\)[/tex]) reacts with oxygen ([tex]\(O_2\)[/tex]) to form potassium oxide ([tex]\(K_2O\)[/tex]). This type of reaction, where two or more reactants combine to form a single product, is known as a synthesis reaction.
Having established the types of reactions for A and B, we can now determine which statement is correct from the given options:
1. Both are synthesis reactions.
2. Both are decomposition reactions.
3. A is a synthesis reaction, and [tex]\(B\)[/tex] is a decomposition reaction.
4. A is a decomposition reaction, and B is a synthesis reaction.
### Conclusion:
- Reaction A ([tex]\(Ca(OH)_2 \rightarrow CaO + H_2O\)[/tex]) is a decomposition reaction.
- Reaction B ([tex]\(4K + O_2 \rightarrow 2K_2O\)[/tex]) is a synthesis reaction.
Therefore, the correct statement is:
- A is a decomposition reaction, and B is a synthesis reaction.
Thus, the correct choice is:
[tex]\[ \boxed{4} \][/tex]
