I have read that the weak force does not obey the charge symmetry, the parity symmetry, and the time reversal symmetry.
Then how does it obey the CPT symmetry?
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We are left with the combination of all three, CPT, a profound symmetry consistent with all known experimental observations.
On the theoretical side, CPT invariance has received a great deal of attention. Georg Ludens, Wolfgang Pauli and Julian Schwinger independently showed that invariance under Lorentz transformations implies CPT invariance. CPT invariance itself has implications which are at the heart of our understanding of nature and which do not easily arise from other types of considerations.
Italics mine. As Lorenz invariance is true for all elementary particle interactions , CPT has to hold.
So you must be confused wity CP violation. With strict CPT invariance, Time reversal will not hold in those decays where CP is violated.
CP invariance was thought to be a general conservation principle until the details of the neutral kaon decay process were examined by Cronin and Fitch. After intense study over many years, the consensus is that CP is violated by a small amount. In 2001 CP violation was confirmed in B-meson decay. It is thought possible by some investigators that in CP violation is to be found the reason for the vast excess of matter over antimatter in the universe.
The small violation of CP symmetry suggests some departure from T symmetry in some weak interaction processes since CPT invariance seems to be on very firm ground.