Why is there no `nand` instruction in modern CPUs?
http://www.ibm.com/support/knowledgecenter/ssw_aix_61/com.ibm.aix.alangref/idalangref_nand_nd_instrs.htm : POWER has NAND.

But generally modern CPUs are built to match automated code generation by compilers, and bitwise NAND is very rarely called for. Bitwise AND and OR get used more often for manipulating bitfields in data structures. In fact, SSE has AND-NOT but not NAND.

Every instruction has a cost in the decode logic and consumes an opcode that could be used for something else. Especially in variable-length encodings like x86, you can run out of short opcodes and have to use longer ones, which potentially slows down all code.