have (sexual) relations (with someone)
To engage in sexual activity (with someone); to have or be in a sexual relationship (with someone). As there was no hard evidence that Mr. Smith's ex-wife had sexual relations outside of marriage, the judge was obliged to uphold the prenuptial agreement during the divorce proceedings. I hear Jim got fired for having relations with his secretary.
have relations with someone
Euph. to have sexual relations with someone. While engaged to Mary, he was having relations with at least two other women. She was having relations with one of her employees, which was strictly against policy.