Comparison of bool data types in C++

§4.5 of the C++ standard says:

An rvalue of type bool can be converted to an rvalue of type int, with false becoming zero and true becoming one.

regarding 2 and 3, type conversion takes place so the statements will work as desired

According to the rule of Boolean conversions:

A prvalue of integral, floating-point, unscoped enumeration, pointer, and pointer-to-member types can be converted to a prvalue of type bool.

The value zero (for integral, floating-point, and unscoped enumeration) and the null pointer and the null pointer-to-member values become false. All other values become true.

Then

bool x = 1; // x will be true
bool y = 0; // y will be false
bool z = 1; // z will be true

For the 1st case, if (x==1), x will be promoted to int,

the type bool can be converted to int with the value false becoming ​0​ and true becoming 1.

then (x==1) is true.

For the second case, if (y>0.5), y will be promoted to int with value 0, then converted to double for the comparison;

If the operands has arithmetic or enumeration type (scoped or unscoped), usual arithmetic conversions are performed on both operands following the rules for arithmetic operators. The values are compared after conversions:

and

If the operand passed to an arithmetic operator is integral or unscoped enumeration type, then before any other action (but after lvalue-to-rvalue conversion, if applicable), the operand undergoes integral promotion.

...

• Otherwise, if either operand is double, the other operand is converted to double

then y>0.5 is false.

For the third case, if (z>0.5), z will be promoted to int with value 1, then converted to double for the comparison; then z>0.5 is true.