diff --git a/changelog/fix_false_positive_for_style_unless_logical_operators.md b/changelog/fix_false_positive_for_style_unless_logical_operators.md
new file mode 100644
index 00000000000..09ad78584ae
--- /dev/null
+++ b/changelog/fix_false_positive_for_style_unless_logical_operators.md
@@ -0,0 +1 @@
+* [#9551](https://github.com/rubocop/rubocop/issues/9551): Fix a false positive for `Style/UnlessLogicalOperators` when using `||` operator and invoked method name includes "or" in the conditional branch. ([@koic][])
diff --git a/lib/rubocop/cop/style/unless_logical_operators.rb b/lib/rubocop/cop/style/unless_logical_operators.rb
index 5f992b8d674..70e86a805fe 100644
--- a/lib/rubocop/cop/style/unless_logical_operators.rb
+++ b/lib/rubocop/cop/style/unless_logical_operators.rb
@@ -87,11 +87,17 @@ def mixed_logical_operator?(node)
         end
 
         def mixed_precedence_and?(node)
-          node.source.include?('&&') && node.source.include?('and')
+          and_sources = node.condition.each_descendant(:and).map(&:operator)
+          and_sources << node.condition.operator if node.condition.and_type?
+
+          !(and_sources.all? { |s| s == '&&' } || and_sources.all? { |s| s == 'and' })
         end
 
         def mixed_precedence_or?(node)
-          node.source.include?('||') && node.source.include?('or')
+          or_sources = node.condition.each_descendant(:or).map(&:operator)
+          or_sources << node.condition.operator if node.condition.or_type?
+
+          !(or_sources.all? { |s| s == '||' } || or_sources.all? { |s| s == 'or' })
         end
       end
     end
diff --git a/spec/rubocop/cop/style/unless_logical_operators_spec.rb b/spec/rubocop/cop/style/unless_logical_operators_spec.rb
index 3a7c66480fd..bd7bbaa8061 100644
--- a/spec/rubocop/cop/style/unless_logical_operators_spec.rb
+++ b/spec/rubocop/cop/style/unless_logical_operators_spec.rb
@@ -116,6 +116,26 @@ def condition?
         return unless a?
       RUBY
     end
+
+    it 'does not register an offense when using `||` operator and invoked method name includes "or" in the conditional branch' do
+      expect_no_offenses(<<~RUBY)
+        unless condition
+          includes_or_in_the_name
+
+          foo || bar
+        end
+      RUBY
+    end
+
+    it 'does not register an offense when using `&&` operator and invoked method name includes "and" in the conditional branch' do
+      expect_no_offenses(<<~RUBY)
+        unless condition
+          includes_and_in_the_name
+
+          foo && bar
+        end
+      RUBY
+    end
   end
 
   context 'EnforcedStyle is `forbid_logical_operators`' do