Only PNG supports transparency, is that true?

Solution 1:

• png-32 supports different levels of transparency. Each pixel can have an opacity between 0 and 255, with 0 as completely transparent.

• png-24 supports setting one color as fully transparent. Everything else will be opaque.

• gif uses a color palette. You can specify that one color in the palette is fully transparent.

• png-8 also uses a color palette but each color in the palette has its own opacity value, so it supports varying levels of transparency too.

• jpg does not support transparency.

Solution 2:

JPEG 2000 supports full transparency. See JPEG 2000 Side channel spatial information.

Solution 3:

JPEG XR (not the same as JPEG 2000) also supports transparency.
However it is not a useful format for the web as only Internet Explorer and Edge support it.

WebP is another emerging image format with support for transparency.
However, Internet Explorer lacks support for it.